The Sun says he would be willing to go back if the takeover by an American consortium is completed.
Allardyce, 64, thinks he has one more top project in him — and has a backroom staff ready to come along.
The imminent takeover will see MSD Partners pump in cash.
Current manager Jack Ross will stay in charge to guide the promotion bid and is guaranteed an extra year if he succeeds.
But the ambitious owners- in-waiting want to get back to the Premier League as soon as possible.
And that could open the door to former Bolton and West Ham chief Allardyce.