But he isn't sure the 60-year-old would be interested in the Black Cats hot seat...
The 60-year-old has been out of work since the summer, when he left West Ham United after the owners chose not to renew his contract at Upton Park.
And many see Big Sam as the perfect successor to Dick Advocaat at Sunderland. If you are aiming high, never hire Allardyce. But, if you want to stay up, always hire him...
Keys wrote: "Nigel Pearson? Sean Dyche? Maybe. Big Sam could with his eyes shut but I don't think the job interests him. Whatever Sunderland do I hope they turn away from the recent trend of appointing foreign managers. It hasn't worked."
There has certainly been plenty of talk linking Allardyce with Sunderland, with Sky Bet making the 60-year-old a 1/1 favourite to move to the Stadium of Light.
Whatever criticism Keys gets, though, and he has been wrong an awful, awful lot, he does know Big Sam personally.
That suggests he may well have an inkling as to whether the Black Cats would tempt the manager. Allardyce may well be enjoying his time out of management and could be treating it like semi-retirement.
Does he need the stress of the impossible Sunderland job?