Parkinson's squad begin their preparations for the 2014/2015 campaign in around two weeks time but Taylor isn't expected to be involved as he continues to recovery from a complex foot injury.
The 32 year-old damaged the plantar plate - a small supporting ligament underneath the toe - during a behind-closed-doors friendly at Leeds United back in early February, forcing the former Charlton Athletic centre half to have an operation to rectify the problem.
He is now out of the protected boot he was initially required to wear after the operation but it is still believed that the beginning of pre-season training will come around too soon for him.
After signing from Charlton last August, Taylor made four appearances for City last season before injury struck.
Taylor, who has a year left on his City contract, also enjoyed a month's loan period with fellow League 1 side Colchester United.