Manchester City manager Pep Guardiola has admitted that his side are still looking to make additions this summer.
Sanchez has been linked with a move away from the Emirates this summer, with the Citizens mooted as a potential destination. "He's staying", Wenger said.
"I am responsible for the global policy of the club but for the players it is different".
A host of top clubs are believed to be interested in signing the former Barcelona forward including PSG, who Sky sources understand are willing to offer him £250,000 per week.
Recent reports have suggested that Sanchez is desperate to depart from the Emirates, with Manchester City, who are hot in his pursuit, his preferred destination.
The 28-year-old posted a picture on his Instagram page on Friday to reveal that he was suffering from sickness, although given that he is now trying to leave the club after turning down Arsenal's attempts to extend his contract beyond the end of next season, plenty of doubt was cast over the severity of his illness.
Deals for Alexis and Ozil are due to expire at the end of the coming campaign, with the Chile global having been linked with Manchester City and Paris Saint-Germain as a result. While the amount is still some way off the staggering £400,000-a-week contract that he has demanded from Arsenal, the deal has various performance-related bonuses as sweetener.
Despite no real shortage of options, the Spaniard is intent pursuing a deal for Sanchez to create a truly formidable squad that can challenge for the Premier League as well as the Champions League. Whether you have two or one years left it doesn't change.
And at 28, he will provide his best years to City. One day [Alexis] will go and Arsenal will go on.