The 27-year-old defender has fallen behind Trent ¬Alexander-Arnold at Liverpool and has been limited to one appearance so far this season.
That came in the Carabao Cup last month, when Jurgen Klopp’s men lost 2-1 to Chelsea.
Clyne knows Alexander-Arnold is ahead of him in the pecking order and is ready to move on to secure regular first-team football.
The Foxes are in the ¬market for a new right-back and are keeping tabs on the player’s situation.
London-born Clyne joined Liverpool from Southampton for £12.5million in 2015 under then-boss Brendan Rodgers and quickly established ¬himself as first-choice right-back.
Rodgers left that October but Clyne initially remained in favour under Klopp and had a spell as England’s first-choice right-back.
Last season, however, he was plagued by injuries, in particular a back problem which required surgery, and he didn’t feature until April – playing five times.
During his time on the sidelines, younger duo Alexander-Arnold and Joe Gomez emerged, and Clyne has not been able to find his way back past them.
That has opened the door to suitors, with Leicester prominent among them.