The 48-year-old German is available having quit Borussia Dortmund at the end of the last campaign and is said to be interested in filling the vacant Anfield post.
Talks between the Merseyside club and Klopp are already underway and Liverpool appear keen to secure a move to bring in the two-time Bundesliga winner to replace Brendan Rodgers as soon as possible.
Following his sacking, which came following Liverpool’s 1-1 draw with Everton on Sunday, Rodgers issued a statement via the League Manager’s Association;
“It has been both an honour and a privilege to manage one of the game’s great clubs,” said the Northern Irishman, who was sacked after Sunday’s 1-1 Merseyside derby draw at Everton.
“I have worked every day to represent the club to the best of my ability, to develop both individual players and a team that the club’s magnificent fans can be proud of.
“There have been some very memorable moments during my time at Liverpool and I would like to thank all of the players for their hard work and commitment.” Rodgers added.
Klopp helped Borussia Dortmund to two Bundesliga titles during his seven year tenure in charge at the Westfalenstadion and also guided the club to a Champions League final in 2013, which they lost to domestic rivals Bayern Munich at Wembley.