The Argentina World Cup winner is set to leave Villa Park this summer and is being linked with Barcelona and Manchester United.
With Martinez now 32, Cutler told The Sun: “This summer is pivotal for Emi in terms of his career.
“He’s been voted the best goalie in the world twice and there seems to be an opportunity for him this summer, with all of his options open.
"Big clubs are queuing up to speak to him and he either stays at a massive club like Villa or he goes to a truly world-class club.
“I don't think it’s about money with Emi so I don’t think he is ready to move to Saudi yet.
“If he does move it would be to a much bigger club — one of the really big-hitters like Barcelona, Real Madrid, Atletico... or even Manchester United.”
Man Utd challenge would suit Emi
Cutler insists Martinez will be influenced by the challenge when choosing his next move.
"United can't offer him Champions League football but the sheer size of the club and the size of the challenge might appeal to Emi," said Cutler, now in charge of Wolves' goalkeepers.
"Emi has the confidence required to play for a massive club like United and would feel he could affect the club in a really positive way.
"He would look at United and say: 'Right, I can make this place better. I can help this club get back to where it was.'
"He's all about the challenge, he's all about the drive and the desire so I think United would suit him.
"He thrives on the biggest occasions and could play for any team in the world as he's shown by winning the World Cup and Copa America with Argentina.
"He would be a comfortable fit at United and would hit the ground running.
"It's all down to what Villa want but, at 32, they will know this is when they can get the maximum return on him. If they hold off until next year they'd get less."