Wenger's future is the subject of renewed scrutiny after the Gunners were beaten 3-0 by Everton at Goodison Park on Sunday to leave their top four destiny out of their own hands.
Goal understands the Frenchman has agreed in principle a two-year extension with Arsenal but he is yet to announce he is staying beyond this summer, when his current deal expires.
|11/10||Everton are 11/10 with William Hill to finish in the top four|
And as talk turns to Wenger's potential successor, Wright believes Martinez ticks all the boxes.
"That's the kind of manager that you want, a good young manager that has proven himself tactically, he knows what he's doing," Wright told BBC Sport.
"It's got to be that kind of man, Roberto Martinez, he's the perfect one. If someone was to ask me who I want, I'd say Roberto Martinez.
"That's the kind of manager you've got to be looking at to take Arsenal forward."
Wenger's men are limping to the Premier League finish line, having taken two points from their last four matches while Everton have won six in a row.
Wright insists it is unacceptable that a traditional 'Big Four' team is fading late in the campaign and can understand why many are contemplating the possibility of Wenger leaving in the summer.
"I feel that like a lot of people out there it is very hard to think of it [Arsenal without Wenger]," he said.
"As they say on social media, be careful what you wish for, but we're in a situation now where Arsenal fans are starting to look into this massive void and it's not looking good.
"This stage of the season the players should be finishing on a high but they're running out of steam."