Alexis, whose current deal expires in 2018, has been linked with Manchester United, Chelsea and Manchester City.
The Chile international is currently locked in a contract stalemate, after the Gunners offered him a new contract worth in excess of £250,000-a-week.
Wenger has made it clear he will not sell the 28-year-old like he did and explained that it is a different situation to when Arsenal sold Robin van Persie to United in 2012.
“I don’t think that you would sell him to any Premier League club, that is for sure. The question is more, Why would you sell him to another [Premier League] club? You want to be as strong as you can be, and not strengthen the other teams.
“I let Van Persie go in the last year of his contract because Van Persie was 29, going on 30 and he was signing a long-term contract. That is not the case with Alexis. I personally think he will sign and stay here.
“Even if he doesn’t sign a new deal, I will make him stay? Yes. Would I rather keep him than sell to a Premier League rival? Yes.
“But first of all, he is happy here. His desire is to stay. That is what I deeply believe.
“The disagreements are more contractual, not on the desire. Both parties have the desire to find an agreement, so I think it will happen,” Wenger said.