The Spanish football federation (RFEF) are considering dismissing Jorge Vilda just nine days after his Spain side won the Women's World Cup.
Acting RFEF president Pedro Rocha is expected to make a decision on Vilda's future by Wednesday.
Vilda applauded Luis Rubiales' controversial speech at the RFEF extraordinary assembly on Friday.
During his speech, Rubiales addressed Vilda directly, calling him the best coach in women's football and offering him a new €500,000-a-year four-year contract.
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Vilda released a statement on Saturday criticising Rubiales but he stopped short of calling for his resignation or dismissal.
The Spain squad said on Friday they would not play for their country again until the leadership at the federation had been removed.
All of Vilda's eleven-strong backroom team resigned on Saturday, leaving the head coach without any players or coaches.
The world champions have Nations League games against Sweden and Switzerland next month.
Meanwhile, Luis de la Fuente's position as men's head coach is thought to be safer even though he also applauded Rubiales' speech. He has also released a statement on Saturday criticising the suspended president.
De la Fuente is expected to name his squad on Friday for Euro qualifiers next month against Georgia and Cyprus.
Vilda has been a divisive figure as head coach of the women's team. Last year, 15 players said they would not play for him again because of concerns about their health and emotional state. Twelve of them missed the World Cup.
Analysis: Vilda doesn't have enough credit in the bank
LaLiga TV's Semra Hunter:
"It doesn't come as a surprise. People have been asking for his head - along with Rubiales - for a long time now
"It's not just him, but Luis de la Fuente, who is the head coach of the men's national team, and pretty much everybody else at the federation who supports Rubiales.
"People here in society are very upset and angry with the way this has played out and they've been demanding there be a proper clear-out.
"A whole new restructuring needs to be put into place with people who actually look after the well-being of these women who will care about women's football and their values.
"It doesn't come as a surprise given that Rubiales has lost so many people in his corner and so many have turned their backs on him.
"Vilda is isolated in this position and I don't think he's got enough credit in the bank to save his job at this point in time."
Spanish football chiefs call for Rubiales to resign
The regional presidents of the Spanish Football Association have requested the immediate resignation of Luis Rubiales.
There has been widespread criticism of Rubiales after he kissed Spain forward Jenni Hermoso on the lips following their 1-0 World Cup final win over England eight days ago.
A statement from the Spanish football federation (RFEF) read: "Once the meeting of the Commission of Presidents of Regional and Territorial Federations of the RFEF has finished, the following agreements are unanimously made known to the world of football and society:
"After the latest events and the unacceptable behaviours that have seriously damaged the image of Spanish football, the presidents request Mr Luis Rubiales immediately present his resignation as president of the RFEF.
"We warmly congratulate the women's soccer team for their victory in the World Cup. We value the meaning and legacy of success for Spanish sport. We express our admiration and gratitude to an unrepeatable group of players and we extend our congratulations to all those who have built, over the years with determination, the growth of women's football.
"We will urge the corresponding bodies to carry out a deep and imminent organic restructuring in strategic positions of the Federation to give way to a new stage of management in Spanish football.
"Once FIFA has suspended Mr Luis Rubiales, the Federation's internal protocols have been activated as a result of the suspension.
"In addition, we have urged President Pedro Rocha to immediately withdraw the last communication on behalf of the Federation with FIFA and UEFA that we have known [on Monday].
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"The RFEF maintains its commitment to continue implementing its investment, as well as equality policies for the development of women's football.
"Lastly, the Presidents' Commission has given its unanimous support to Mr Pedro Rocha so that he may lead a new stage where dialogue and reconciliation with all football institutions is the line to follow. We make ourselves available to the CSD and all the institutions involved to continue building together the candidacy for the 2030 World Cup."
Hermoso released a statement on Friday saying she felt vulnerable and had been "a victim of an impulse-driven, sexist, out-of-place act without any consent on my part".
Rubiales was widely expected to resign from his role as Spanish FA president on Friday but instead made a defiant speech, claiming he was the victim of a witch-hunt by "false feminists".
As a result, the Spanish FA called an "extraordinary and urgent" meeting on Monday "to evaluate the situation in which the federation finds itself".
Rubiales has been suspended by FIFA, while the Spanish FA's own request for the federation to be suspended by UEFA has been rejected after it complained the Spanish government was interfering in its affairs.
The crisis also took a bizarre turn on Monday morning with Rubiales' mother, Angeles Bejar, locking herself in a church in Motril, and refusing to eat because of the "inhuman hunt" against her son.
Spain prosecutors have also opened a preliminary investigation into Rubiales on the grounds him kissing Hermoso could constitute a crime of "sexual assault".
The Prosecutors' Office of the National Court had received six complaints but was waiting for one from the player before opening an investigation.
Spain boss Vilda condemns Rubiales behaviour
The fallout from the incident has also led to Spain women's coaching staff resigning en masse - with the exception of head coach Jorge Vilda.
But Spain's World Cup-winning boss has since broken his silence on events and criticised suspended Rubiales, calling the kiss "inappropriate and unacceptable".
Spain assistant managers Montse Tome, Javier Lerga and Eugenio Gonzalo Martin were among those to have decided to stand down from their positions.
Physiotherapist Blanca Romero Moraleda and goalkeeper coach Carlos Sanchez, plus half a dozen others at several age-group levels, have also tendered their resignations.
Jorge Ivan Palacio, the chairman of the FIFA disciplinary committee, last week ordered Rubiales and the Spanish FA to refrain from contacting or trying to reach Hermoso, either directly or through intermediaries.
Hermoso accused the Spanish FA of a "manipulative, hostile and controlling culture" as a total of 81 players signed a letter stating they will not accept national team call-ups while Rubiales remains in situ.
Rubiales also grabbed his crotch in celebration despite being just metres away from Spain's Queen Letizia and her teenage daughter in the stadium VIP area.
Rubiales apologised for his behaviour in the VIP section but insisted in his speech on Friday he had been the target of a "social assassination" and repeatedly and emphatically stated "I will not resign", words that drew applause from the gathered delegates at an extraordinary general assembly of the Spanish FA.
Rubiales claimed the incident was "spontaneous, mutual, euphoric and consensual" but Hermoso, who previously suggested comments playing down the incident attributed to her by the federation were false, hit back with an attack on the organisation as a whole.
"It is not up to me to evaluate communication and integrity practices, but I am sure that as the world champion national team we do not deserve such a manipulative, hostile and controlling culture," she said in a statement.
"I want to reinforce the position I took from the beginning, considering that I do not have to support the person who has committed this action against my will, without respecting me, at a historic moment for me and for women's
sport."