Roberto Martinez is now the 15/8 favourite with Sky Bet to be the next Everton manager after Wigan's relegation from the Premier League was confirmed.
A 4-1 defeat at Arsenal sent the FA Cup winners down to the Championship but Martinez could be set to stay in the Premier League with a switch the Toffees.
The Goodison Park club's search for David Moyes' replacement has seen Martinez at the head of the betting throughout, although Gus Poyet has come in to 6/1 from 25/1 following Brighton's failure to reach the Championship play-off final.
Celtic manager Neil Lennon (7/2), former Everton favourite Alan Stubbs (16/1) and Cardiff boss Malky Mackay (20/1) are some of the other names in the frame.
Meanwhile, Wigan are 4/1 to bounce straight back to the Premier League next season and 11/1 to win the Championship title.
Arsenal's victory propels them into pole position for the final Champions League spot ahead of Tottenham and Arsene Wenger's men are 4/11 for a top-four finish.
Spurs are available at 2/1 as they sit one point behind the Gunners ahead of the final day of the campaign.
Sky Bet football trader Chris Spicer said: "Roberto Martinez may now decide the time is right to move on to pastures new should Everton come calling.
"If he stays at Wigan it is no sure thing they will come straight back up, you just have to look at Blackburn, Bolton and Wolves this season."
He added: "Arsenal will surely need to get a victory at Newcastle on Sunday, with Spurs hosting Sunderland a draw likely won't be enough so we're in for an exciting final day in the race for fourth."