Liverpool have sacked manager Brendan Rodgers after three and a half years in charge.
Ex-Borussia Dortmund boss Jurgen Klopp is first choice to take over.
Rodgers was dismissed after Sunday's 1-1 draw at Everton, which left the Reds 10th in the Premier League, but the decision was made before the game.
"Although this has been a difficult decision, we believe it provides us with the best opportunity for success on the pitch," read a club statement.
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Former Chelsea and Real Madrid manager Carlo Ancelotti and Ajax boss Frank de Boer have also been linked with the Liverpool job in recent weeks.
"The search for a new manager is under way and we hope to make an appointment in a decisive and timely manner," added the statement.
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.
Northern Irishman Rodgers, who took over in June 2012, led Liverpool 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.
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His departure came on the day when Sunderland boss Dick Advocaat resigned.
Liverpool are owned by Fenway Sports Group and a joint statement from principal owner John W Henry, chairman Tom Werner and president Mike 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 have left Liverpool during Rodgers's tenure.
Liverpool reached the FA Cup semi-finals last season but won only one of their final six league games, including a 6-1 hammering at Stoke in the final match.
|BBC Sport's Ben Smith:|
|"Fenway Sports Group's decision to sack Rodgers was made before today's Merseyside derby, but the owners did not want to disrupt preparations for the match by making an announcement before the game. Even a victory at Goodison Park would not have prevented Rodgers losing his job.|
|"Rodgers was not told at Goodison Park. He was visited at home by Ian Ayre and I am told he took the news with dignity and good grace. Many of the players are now off on international duty and so there was was no chance to say goodbye to them."|
Rodgers is the first Liverpool manager since the 1950s not to win a trophy in his first three seasons. He finished seventh, second and sixth in the Premier League.
Liverpool spent about £80m in the summer as Rodgers signed Christian Benteke, Danny Ings, Roberto Firmino, Nathaniel Clyne and Joe Gomez.
'The spark had gone' - how the experts reacted
BBC Sport chief football writer Phil McNulty: "The mood of Brendan Rodgers shortly before he was sacked as Liverpool manager was in keeping with his demeanour this season. Rodgers insisted he was not feeling pressure and fired off a few salvoes of self-defence, insisting Liverpool would improve in the months ahead.
"And yet, as there has been all season, there was a sense a spark was missing from a young manager who exuded positivity from the moment he walked into Anfield in the summer of 2012. It was almost as if he was on auto-pilot, not as a manager but with the media.
"Rodgers looked tired and drawn, perhaps easy to say with hindsight, but actually did not give the impression he knew what was coming in the next hour.
"He drew a deep breath as he left his final inquisition as Liverpool manager - walking out of the door at Goodison Park and within an hour out of the door at Anfield."
Former Newcastle striker Alan Shearer on MOTD2:
"No-one wants to see a manager get sacked but the bar was set when the owners sacked Kenny Dalglish for finishing eighth, getting into two cup finals and winning one of them. From there to now I don't really see much progression.
"Looking from the outside now, I don't seen an identity, I don't see who their best players are, what the plan is or what the best system is. So from that point of view I was pretty confused.
"From the beginning of this season, with his two coaches going I thought Brendan was a dead man walking. As soon as he was going to have a bad run I felt the inevitable would happen."
Former England striker and BBC Radio 5 live 606 host Ian Wright:
"I am shocked. He was meant to be the new kid on the block but he had run out of time.
"It is unfortunate for him but I don't think Liverpool owed him that time. They gave him a lot of money to spend.
"The club are nowhere near where they want to be. A club of Liverpool's size do not need to answer to anyone."
Former Liverpool captain Jamie Carragher on Sky Sports:
"Rodgers can't argue in some ways. He's been there three years, he hasn't won a trophy and they've played Champions League football once. That's not good enough for Liverpool.
"Liverpool are becoming Tottenham. They think they are a big club but the real big clubs aren't concerned about what they do. What are these owners going to do to get the club back to where it needs to be?"
Swansea manager Garry Monk, who played under Rodgers at the Liberty Stadium:
"I cannot believe it. I don't understand it. It is a very harsh decision and he did not deserve that at all.
"He is a top manager. You do not know what happens behind closed doors. I am not sure who would do a better job at Liverpool.
"He will bounce back. He was so supportive to me, giving me advice when I got the job [at Swansea]. He is a top man and a top manager."
Arsenal boss Arsene Wenger:
"I'm always sad when that happens as I think he is a quality manager. Unfortunately the pressure is always bigger on the managers.
"He was very unlucky to not win the Premier League. He was closest certainly to winning the Premier League of all the managers that have been working for the club, but that is the way it goes now and I wish him good luck. I'm sure he will find a job again."