Liverpool have reportedly contacted representatives of former Borussia Dortmund Jurgen Klopp as well as Carlo Ancelotti, according to SkySports.
The club sacked Brendan Rodgers on Sunday and are keen to name a replacement in time for their next fixture after the international break.
They play Tottenham on October 17 in a Premier League fixture.
But Liverpool plan to appoint a new manager before they go to Tottenham on October 17 after the international break and have no plans to appoint a caretaker as they hope to have the vacancy filled.
Klopp and former Chelsea boss Ancelotti are currently not attached, after Klopp left Borussia Dortmund at the end of last season and Ancelotti was sacked by Real Madrid in the summer.
It emerged last month Klopp is keen on working in the Premier League, while Ancelotti won the title during a two-year spell at Chelsea