Giggs has been out of work since leaving Manchester United's coaching set-up in the summer, but Gray believes that the Welshman could emulate former teammate Roy Keane as manager of the Black Cats.
"He may have had a little bit of a falling out with the players and fans towards the end, but I don't think you can forget what Roy brought to Sunderland," he told talkSPORT.
"He was the one who got the club back into the Premier League and that was his first job – I think Ryan Giggs would have the same effect. I'm not dissing David Moyes here, I'm not trying to get him out of the job.
"All I'm saying is that if there was an opportunity to bring Ryan in, I would take him."