Graham Rodger, Grimsby's assistant manager said: "Jermaine gave a good little account of himself at times - he's certainly worth another look.
"To say he had a good game against Manchester United tells you that he's not a bad player."
Palmer has spent this season in City's reserve team other than one occasion against Sunderland in November where he was substituted onto the pitch in the 89th minute to replace Clint Hill.
He has impressed on a few occasions in the reserve team though. Palmer looks confident and skillful and a move to Grimsby could be a good one for him.