The 21-year-old shot-stopper was released by City at the end of last season after failing to make a first-team appearance for the club.
Alex believe they will only have one of their current keepers on their books for the start of the 2008-09 campaign.
Ben Williams has already opted to leave the club while Owain fon Williams is expected to follow suit, leaving only Stuart Tomlinson as a recognised keeper.
Legzdins was loaned out to Alfreton Town, Halifax Town, Oldham Athletic and Macclesfield Town during his time at St Andrew's.