Liverpool are interested in Jurgen Klopp and Carlo Ancelotti as the search begins for a new manager, according to Sky sources.
Brendan Rodgers was sacked hours after a 1-1 draw at Goodison Park in the Merseyside derby left Liverpool with just one Premier League win since August.
A statement from the owners said "the search for a new manager is already under way" and, although neither has yet been contacted it is understood both Klopp and Ancelotti are in the frame.
It is not clear at this stage whether other potential candidates are being considered, but Liverpool plan to appoint a new manager before they go to Tottenham on October 17 after the international break and have no plans to appoint a caretaker as the hope to have the vacancy filled.
Both Klopp and Ancelotti are currently out of work, Klopp after leaving Borussia Dortmund and Ancelotti after he was let go by Real Madrid in the summer.
It emerged last month Klopp is keen on working in the Premier League, while Ancelotti won the title during a two-year spell at Chelsea.
It is understood, meanwhile, that Rodgers went into the Everton game unaware he would be dismissed and was informed of the decision in a telephone call with the club's owners some time after the game.
He then held a meeting with chief executive Ian Ayre.