Liverpool hope to appoint Jurgen Klopp to replace sacked manager Brendan Rodgers by the end of this week.
The former Borussia Dortmund coach is favourite to take over from the Northern Irishman, with ex-Chelsea boss Carlo Ancelotti also a contender.
German Klopp, 48, is understood to be open to the idea of a move.
Talks with his representatives are progressing well and the club want a new manager in place to prepare for a visit to Tottenham on 17 October.
In a statement issued by the League Managers’ Association on his behalf, Rodgers, 42, said he was “incredibly disappointed” his three-and-a-half-year tenure at Anfield was over.
“It has been both an honour and a privilege to manage one of the game’s great clubs,” said the Northern Irishman, who was sacked after Sunday’s 1-1 Merseyside derby draw at Everton.
“I have worked every day to represent the club to the best of my ability, to develop both individual players and a team that the club’s magnificent fans can be proud of.
“There have been some very memorable moments during my time at Liverpool and I would like to thank all of the players for their hard work and commitment.”
Rodgers, who said he is in no rush to take another job, added the Reds squad was in transition but was showing a “strong sense of togetherness”.
Negotiations will now take place over his severance package, which could cost Liverpool in excess of £5m.
Assistant boss Sean O’Driscoll, first team coach Gary McAllister and development coach Pep Lijnders took training for Liverpool’s non-international players at the club’s Melwood complex on Tuesday.