The Chile international’s future has been under constant speculation during the summer transfer window.
With less than a year left on his current deal, no extension appears forthcoming.
However, Arsenal are prepared to let Sanchez run his contract down to get one more season out of their forward.
Manchester City, Chelsea and Paris Saint-Germain are all interested in the ex-Barcelona star.
But Wenger is determined not to strengthen one of his title rivals by selling Sanchez.
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Arsene Wenger believes Alexis Sanchez will stay at Arsenal and fight for the title this term
It's always in your interests, even if you have a short contract, to do well
Arsene Wenger
And with Arsenal looking to bounce back from their fifth-place finish, Wenger is convinced Sanchez is ready to challenge for top spot at the Emirates.
Asked whether he was confident that Sanchez will give everything to the team if he remains at the club this summer, Wenger replied: "Of course. Why not?
“If you look at it, it's always in your interests, even if you have a short contract, to do well.
“And the kind of character he is [also convinces me].
"He is a winner. When he goes on the football pitch, he wants to win.
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Manchester City and PSG are among the clubs keen to sign Alexis Sanchez from Arsenal
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“He is a guy who loves football. He has advantages and disadvantages on both sides going into a situation like that.
"When you have made 75 points (last season), your target is to get 10 points more. And with 10 points more, you are in there (the title race)."
Arsenal are still in talks with Monaco over winger Thomas Lemar ahead of the new season.
