Liverpool's American owners FSG had reportedly made the decision to sack manager Brendan Rodgers prior to Sunday's Merseyside derby.
The Northern Irishman, who failed to win a trophy in his three years in charge at Anfield, was dismissed by the club on Sunday.
Rodgers learned of his fate three hours after Liverpool's 1-1 draw against Everton, but according to BBC Sport, the owners would have sacked the 42-year-old regardless of the result at Goodison Park.
It is believed that poor results, including back-to-back draws in the Europa League and scraping past Carlisle United on penalties in the Capital One Cup, pushed the owners into making the change.
The club reportedly hope to make an appointment before Liverpool's next Premier League game, which is against Tottenham Hotspur on October 17 after the international break.
Former Borussia Dortmund boss Jurgen Klopp is expected to hold talks with the Reds this week.