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.
Big Sam told the Sun: “Sunderland are a great club so of course I’d be interested in talking to them.
“I have huge respect for the chairman Niall Quinn and the job he has done.
“I enjoyed the year I had at Sunderland and also when I did some coaching work there under Peter Reid.
“I also know how enjoyed the year I had at Sunderland as a player and also when I did some coaching work there under Peter Reid.
“I also know how passionate the fans are about their team.”
