Mitchell's former boss at Stair Park, Stephen Aitken, has admitted defeat in trying to lure the keeper to his new club Dumbarton.
Aitken said: “When I looked at the goals against column from last season I knew that signing a goalkeeper for Dumbarton was a priority as Danny Rogers has returned to Aberdeen.
“I obviously know David well after working with him for the past few years so I made a quick call to see if being our No.1 was of interest.
“He has not signed for Dundee however there has been a lot of detailed talks so he did not want to jeopardise the chance of full-time football there.”