The former Manchester United and Everton boss has had a nightmare start at the Stadium of Light, picking up just one point from their opening four Premier League games.
The Black Cats have been regular relegation contenders since their return to the top flight in 2007.
And with another fight on the cards, Kilbane – signed by then Everton boss Moyes FROM Sunderland in 2003 – has told Short to give him time to repair the damage.
He said: “David and Sunderland are the perfect fit. But everyone has to be realistic. There were difficulties in the transfer market which stemmed from David getting the job so late. He wasn’t able to get his No.1 targets.