The Chile playmaker proved his worth to the Gunners yet again by firing them into the FA Cup final with the winner against Manchester City on Sunday.
Both City and Manchester United and a host of European clubs have been linked with big money summer moves for Sanchez whose current deal has one more year to run.
But Gunners boss Wenger believes the 24-goal hitman wants to stay, and flatly ruled out any possible sale to a Premier League rival.
"I personally think he will stay and sign," said Wenger. "First of all he is happy here, his desire is to stay, that is what I deeply believe. Both parties have the desire to find an agreement so I think it will happen."
Reports claim United have put Sanchez on their wishlist while City boss Pep Guardiola is understood to be keeping tabs on the situation, but Wenger had bad news for both, saying: "I don't think you would sell him to any Premier League club, that is for sure.
"The question is why would you sell him to another club? You want to be as strong as you can be and not strengthen the other teams. But as I have said, I think he will stay and sign a contract."