Owen Coyle departed the Trotters, who after being relegated from the Premier League last season, sit 18th place in the Championship.
Wanderers' chairman Phil Gartside is now drawing up candidates for the job, and it seems as though Big Sam is among those names listed.
But why would Allardyceleave the Premiership to join Bolton?
He enjoyed a successful eight years in the hot seat at the Reebok Stadium before controversially taking the management job at Newcastle United.
Although Allardyce quit the club, it would seem that Gartside would still like Big Sam to move back north.