The winger's contract has expired and he is not being offered new terms by the Foxes.
The 21-year-old spent the last two months of the season on loan with City, scoring in the last of his eight appearances. Peter Taylor originally signed him with a view to a permanent move, but it is unknown whether or not Reeves has impressed Peter Taylor enough to earn a contract.
Elsewhere, ex-Tiger Ben Petty has been released by Burton Albion. However, manager Nigel Clough could be bringing in another former City defender, with Ian Wright in talks after being released by Hereford.