The Spaniard has further enhanced his reputation during his debut season with Everton, guiding the Toffee’s to seventh place, behind Manchester United on goal difference and with a game in hand.
Martinez has also impressed Wenger and the rest of the Arsenal hierarchy with the style he has implemented on his teams, as well as the way he handles himself.
Martinez is believed to enhanced his credentials further with his dignified reaction to the 4-1 defeat to Arsenal last weekend in the FA Cup quarter finals.
Arsenal are set to confirm Wenger has signed a new two year extension at the Emirates, with his current deal set to expire at the end of the season.
But talks with the club are understood to have already begun over whether Martinez would make a suitable long term replacement.
He was appointed on a four year contract at Goodison Park in the summer, following David Moyes’ move to Manchester United.
Wenger spoke earlier this month about the respect he has for the job Martinez has done at Goodison Park this season.
“Martinez has done remarkably well,” the Frenchman said.