The Bournemouth manager has become joint second-favourite with the bookmakers, alongside Hibernian boss and former Toffees star Alan Stubbs, to take over in the event of the Spaniard leaving Everton.
It comes after a weekend in which Howe masterminded a 5-1 victory over Fulham at Craven Cottage that helped move the Cherries back into contention for automatic promotion.
Bournemouth are currently top of the Championship on goal difference and are next in action against Blackpool – currently bottom of the division and 17 points from safety.
Howe previously left the south coast club for a stint at Burnley but, despite laying the foundations for the Clarets side that secured promotion under Sean Dyche, he opted to return to the Cherries in 2012.
A Bournemouth man through-and-through, having played over 200 games for the club as a defender, Howe would nevertheless find it difficult to turn down an opportunity to manage Everton in the Premier League.
Promotion with the Cherries could possibly put the dampeners on any Goodison Park move but, should Bournemouth fail to go up, the 37-year-old could surely be convinced to switch to the Toffees.
According to Oddschecker, the Championship manager is 12/1 to take over from Martinez, with Laudrup remaining the favourite for the Merseyside post at 8/1.
David Moyes, Duncan Ferguson, Carlo Ancelotti and Jurgen Klinsmann are also available around that same price, as speculation mounts regarding the current Everton manager’s future.