The 31-year-old is still registered as a player, but has been unable to get enough match action to be fit enough for Irn-Bru First Division duty.
The former Rangers, Hibernian and Scotland defender had an operation during the summer to cure a groin problem.
He has completed just 45 minutes of reserve action, a 1-0 defeat at home to Livingston last month, since being named as Alan Adamson's successor at the Bet Butler Stadium.
The Sons still have a reserve outing against Queen of the South to play before they have fulfilled all of their fixtures and Murray is keen to get back in action.
He said: "It's frustrating I have not had much game time as I wanted to be back playing by now.
"We let a few players go in the January transfer window so the squad is very low in numbers.
"So the sooner I can help out the better, but I need games to get myself match-fit."