Liverpool have made contact with representatives of Jurgen Klopp and Carlo Ancelotti, Sky sources understand.
The club are keen to appoint a successor to Brendan Rodgers, who was sacked on Sunday evening, as quickly as possible.
Rodgers was sacked following the 1-1 draw with Everton in Sunday afternoon's Merseyside derby - a result that left the Reds with just one win in their last nine games.
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.
Both Klopp and Ancelotti are currently out of work, Klopp after leaving Borussia Dortmund and Ancelotti after he was let go 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.