Logan is the club's longest-serving player having joined the Foxes' academy ranks in 2001.
Despite over a decade at Leicester the former Republic of Ireland youth international has made just 29 appearances for City.
Loan spells at Boston, Luton, Bristol Rovers, Rotherham and Stockport, with whom he won the League Two play-off final at Wembley in 2008, has seen Logan play more than 150 matches in total.
The 27-year-old last season captained Steve Beaglehole's development squad to the League Two North title.
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