Juergen Klopp and Carlo Ancelotti are the leading candidates to succeed sacked Liverpool manager Brendan Rodgers, according to reports in the British media on Monday.
Rodgers, 42, was sacked on Sunday after a 1-1 draw with Everton left Liverpool 10th in the Premier League table, albeit only three points below the Champions League places, following a sixth-place finish last season.
Klopp, 48, has been out of work since stepping down at Borussia Dortmund at the end of last season, while 56-year-old Ancelotti, who previously worked in England with Chelsea, was sacked by Real Madrid last May.
Several news outlets, including Sky and the BBC, reported that Klopp was the frontrunner, having led Dortmund to two Bundesliga titles and a Champions League final appearance in 2013.
Announcing Rodgers' departure, Liverpool's American owners Fenway Sports Group said: "The search for a new manager is under way and we hope to make an appointment in a decisive and timely manner."
Rodgers, who took over in June 2012, led Liverpool to a second-place finish in the Premier League in 2014.
But Liverpool have since lost Luis Suarez, Steven Gerrard and Raheem Sterling and despite significant investment in new players, Rodgers struggled to reproduce a winning formula.
"Liverpool need a manager who is big enough to handle the pressure, without thinking he is bigger than the club," former Liverpool defender Mark Lawrenson wrote in an article for the BBC.
"Whoever it is will have to buy into the mindset of the American owners -- they want success, but their model is to try to get that by signing younger players they can train up and, sometimes, sell on.
"Juergen Klopp is the favourite to get the job and he would fit the bill.
"At Borussia Dortmund he built a team that were in your face, with good players that he was making better, but he also knew he would have to sell one or even two every year."