The 31-year-old confirmed that he will end his stay on the South Coast this summer after joining the club from Chelsea, initially on loan, in 2014.
Bertrand has attracted interest from Arsenal, AC Milan and Monaco, but the Daily Mail reports that he has decided to move to the King Power, with the Foxes having struggled with injuries at left-back.
Bertrand suffered with injuries early on in his Southampton career but featured 29 times for Ralph Hasenhuttl's side in the Premier League last season.
In total, Bertrand has scored eight goals and provided 20 assists in 240 games for the Saints. body check tags ::