The 32-year-old has been linked with a move to Old Trafford this summer with Villa demanding a fee of £40 million for his services.
Martinez could still leave the club, and former Chelsea midfielder Petit believes his old club should move to sign him.
Speaking to EscapistMagazine.com, Petit said: "Emiliano Martinez would be an inspiration in the Chelsea dressing room. I have criticised his behaviour in the past but he knows what it takes to win titles; he has that experience.
“He can inspire other players and he has all the qualities needed of a top goalkeeper. He would be a very good signing for Chelsea and 32 isn’t old for a goalkeeper.
“I think he’d link well with Enzo Maresca and the players already at the club. One fear I have is for Aston Villa, I am worried about them with top players leaving the club, I’m not sure where it will leave them next season."