The former England defender is a free agent after allowing his contract at Southampton to expire and Leicester are confident they have won the race for the left-back, who turns 32 next month, says the Daily Mail.
Rodgers identified Bertrand - who he coached at reserve and youth level at Chelsea - as the experienced full-back he needed to compete with youngster Luke Thomas.
James Justin, who can also play in that position, is recovering from a serious knee injury while Christian Fuchs departed at the end of last season.
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