Former Borussia Dortmund boss Jurgen Klopp is Liverpool’s first choice to replace Brendan Rodgers, who was sacked after Sunday’s 1-1 draw at Everton.
The Northern Irishman was dismissed following almost three-and-a-half years in charge, with the Reds in 10th position in the Premier League.
No deal has yet been done with Klopp, 48, who won two German Bundesliga titles with Dortmund.
Ex-Real Madrid boss Carlo Ancelotti, 56, is also being considered.
“The search for a new manager is under way and we hope to make an appointment in a decisive and timely manner,” said a Liverpool statement announcing the departure of 42-year-old Rodgers.
The replacement, when he is appointed, will work within the existing structure and what has become known as Anfield’s “transfer committee”.
It is the group that plots and carries out transfer strategy and up until Sunday night consisted of Rodgers, scouts Dave Fallows and Barry Hunter, the man in charge of analysis Michael Edwards, FSG’s Anfield representative Mike Gordon and chief executive Ian Ayre.
One of the big reasons for making the change was that owners FSG firmly believe someone else can get better results with the existing players and within that structure. In other words, they believe it is a squad that can and will perform better under someone other than Rodgers.
Liverpool have won only four of their 11 games in all competitions this season, including victory on penalties against League Two Carlisle at home in the Capital One Cup.
Rodgers, who took over in June 2012, led the Reds to second place in the Premier League in 2013-14. They were top of the table with three games remaining, before losing out to Manchester City.
Liverpool are owned by Fenway Sports Group and a joint statement from principal owner John W Henry, chairman Tom Werner and president Gordon said: “We would like to place on record our sincere thanks to Brendan Rodgers for the significant contribution he has made to the club and express our gratitude for his hard work and commitment.
“All of us have experienced some wonderful moments with Brendan as manager and we are confident he will enjoy a long career in the game.
“Ambition and winning are at the heart of what we want to bring to Liverpool and we believe this change gives us the best opportunity to deliver it.”
Rodgers said this week that he was “not worried” about the possibility of the sack, despite Liverpool’s poor start to the season.
After the draw with Everton, he spoke of a “constant rebuilding” job and highlighted the impact of losing “four real catalysts” of his side – Jamie Carragher, Luis Suarez, Raheem Sterling and Steven Gerrard.