The reserve team coach at Goodison Park has emerged as a favourite to succeed Terry Butcher in the Easter Road dugout, with some bookmakers even going as far as to suspend betting over the post.
Publicly, Everton were refusing to comment on the speculation last night but sources close to the Merseyside club have indicated the 42-year-old former Celtic defender has been in contact with Hibs.
Ian Murray, the Dumbarton manager, Stuart McCall of Motherwell and the former Celtic assistant manager Mark Venus have all been linked with the position since Butcher was sacked last Tuesday.
It is thought Stubbs, who played for Celtic between 1996 and 2001, is the ideal candidate for the new chief executive Leeann Dempster as she looks for a manager to nurture the club's youngsters.
Paul Kane, leader of the Petrie Out campaign, has sent two proposals to the Hibs owner Sir Tom Farmer, but has told supporters he cannot yet divulge what they are.
After a meeting with Farmer and the chairman Rod Petrie - the subject of fans' ire - Kane was asked to put down his ideas for the club's future on paper.