Liverpool parted company with manager Brendan Rodgers on Sunday, just eight games into the Premier League season with the five-times European champions in 10th place.
“Although this has been a difficult decision, we believe it provides us with the best opportunity for success on the pitch,” the club said in a statement.
“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.
“The search for a new manager is underway and we hope to make an appointment in a decisive and timely manner.”
The club have won only three of their opening league games, against Stoke City, Bournemouth and Aston Villa, and count a 3-0 thrashing at home by West Ham United among their early results.
Liverpool also needed a penalty shootout to overcome fourth-tier Carlisle United in the League Cup at Anfield after being held to a 1-1 draw at Anfield after extra time.
(Editing by Ken Ferris)