The veteran left back is not going to renew his contract at the St. Mary's Stadium club.
He will be a free agent and can make a move to any team in the world.
Per Sky Sports, 31-year-old Bertrand wants a new challenge and is of interest to the Foxes.
Arsenal have an interest as well - while Tottenham were linked with a move in January.
Bertrand also has a history with Chelsea, where he came through the youth setup.