The striker wants to see his Sunderland manager stay at the Stadium of Light though.
England will be searching for their new manager in the coming months after parting company with Roy Hodgson on Monday.
He left his role after the Three Lions crashed out of Euro 2016 following an embarrassing 2-1 loss to Iceland at the last 16 stage. The search is likely to be an extensive one for those in charge as they assess their options carefully.
Allardyce is one name that has emerged on the bookmakers' list of potential candidates and Defoe has shared his thoughts about that suggestion.
“He should be among the contenders for the job,” he told BBC Radio 5 Live.
“Obviously I hope he stays at Sunderland. Maybe he could do both. It’s not until you play for a manager that you actually realise what they bring to a team and bring to a dressing room.”
It will certainly be interesting to see who England decide to turn to as their next manager. If they are looking for an elder statesman once again then they could certainly do a lot worse than Allardyce.
He has proved his credentials time and time again in the Premier League, and did so once again last season with Sunderland.
The only concern surrounding him is the so-called long ball football he employs, which is likely to go against him among those who are obsessed with playing like Spain.