"Skysports.com understand that the former Newcastle United and Bradford City playmaker is looking for pastures new after ending a short spell with Nationwide Conference side Aldershot Town.
Tinnion played eight matches for the Hampshire non-leaguers after joining them back in November following a brief training spell with League Two side Cheltenham Town.
He ended a 12-year association with The Robins in September after an unsuccessful managerial spell, despite being regarded as a playing legend at Ashton Gate.
With the January transfer window now open, the 37-year-old is understood to want another spell as a player with a league side.
It remains to be seen if the veteran midfielder can find a new club before the current window shuts this month."
There has been noting on the official Shots website about the player wanting a move.