Roy Keane quit as boss of Sunderland on Thursday and reports link Allardyce, who was axed as manager of Newcastle 10 months ago, with the job.
Nolan said: “I would definitely give the job to Sam if I was Sunderland chairman — no doubt about it. I know he could sort them out and has to be a strong candidate.
“I was sad to see what happened at Newcastle. I’m sure if he’d been given time they would have really developed under his guidance because he’s a top manager. He deserves a big job.”
