Liverpool want to have a new manager in place by the time they play their next Premier League match -- with Jurgen Klopp the early front-runner for the job.
Brendan Rodgers' sacking as the Reds boss was confirmed after their 1-1 Premier League draw at neighbours Everton on Sunday.
Sources have told ESPN FC that there will be no immediate announcement as to who will succeed Rodgers, with approaches to be made to candidates over the coming days.
But Liverpool's American owners Fenway Sports Group want the new manager appointed in time for their trip to Tottenham on Oct. 17.
The club have so far given no indication as to who the next manager will be, but are expected to contact Klopp over the vacancy.
Klopp pledged to take a year's break from football after leaving his post at Borussia Dortmund in May, but is believed to have indicated that he wants to manage in the Premier League.
He won two Bundesliga titles with Dortmund in 2011 and 2012 and guided them to the 2013 Champions League final, having taken over a club in 2008 who had just finished 13th in the German top flight.
Carlo Ancelotti is another manager who would be considered for the job if available.
Ancelotti -- who has coached teams to league titles in Italy, England and France, as well as lifting the Champions League trophy three times as a manager -- is out of work after being sacked by Real Madrid at the end of last season.
But he suggested in May that he needed a year off to recover from back surgery, and reports in Italy have suggested that he is not yet ready to return to management.
While Liverpool seek a new boss, assistant manager Sean O'Driscoll and first-team coach Gary McAllister remain at the club and will take training during the forthcoming international break.
O'Driscoll and McAllister only joined the club in July, as part of a reorganisation of Rodgers' backroom team that followed a poor finish to last season.