Chris Coleman and Gary Rowett are at the top of Swansea’s managerial shortlist to replace Bob Bradley, according to Sky sources.
The club's chairman Huw Jenkins remains a fan of Ryan Giggs, who has been linked with the role, and will discuss potential candidates in the next 48 hours before making any approaches.
Swansea ended Bradley's tenure on Tuesday after just 11 matches in charge following the 4-1 defeat to West Ham and the American was at the Fairwood training centre this morning to say goodbye to his players.
Former Birmingham City manager Rowett and ex Leicester City boss Nigel Pearson are interested in talking to Swansea about the vacancy but Harry Redknapp is not in the running, according to Sky sources.
It comes after Redknapp revealed he was interested in the Swansea job.
"I think if the opportunity and the challenge came up it would be one that would be interesting," the 69-year-old told talkSPORT.
"It's a good club Swansea. Where they've come from and what they've done.
"I've not heard anything, I've had no approach from anybody but it's a good club.
"I still think they've got a chance of staying up, it'll be tight, but they've got a chance."
Meanwhile, former Chelsea defender Mario Melchiot believes Alan Pardew is the right man for the job at the Liberty Stadium because of his top-flight experience.
Speaking on the Premier League Daily, the Dutchman said: "This is a guy who just lost his job [at Crystal Palace], I am sure he's still bitter about that.
"Him going there, I think he can turn it around.
"Alan Pardew has enough experience in this situation and will remain calm."
West Brom coach Gerry Francis told the programme he would go for an experienced candidate over a younger manager like Manchester United legend Giggs.
"Given the situation, you need someone who knows what they are doing very quickly," he said.
"For me, Garry Monk did a fantastic job, look at what he's doing at Leeds at the moment, they made a mistake.
"If they kept with Monk a little bit longer they might not be in this position because he showed he can organise and get teams sorted out."
Speaking to Sky Sports last week, Wales boss Coleman said he is more likely to work in club management abroad.
Coleman, who played for the Swans for four years, said: "I can't say my number one priority is to work in the Premier League.
"It's a great league. If another offer came from there, who knows.
"I think more about working abroad again as realistically you are not going to get one of the big [jobs] in the Premier League."
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