The Chile international looked set for a reunion with Pep Guardiola during the previous transfer window, but the Gunners' failure to land Thomas Lemar from Monaco reportedly persuaded Wenger to keep hold of his prized asset.
Arsenal run the risk of losing Sanchez for free at the end of 2017-18 with his contract due to expire, prompting many to suggest the club could cash in if City return with another bid in the new year.
Ahead of the teams' Premier League clash at the Etihad Stadium on Sunday, Wenger refuted suggestions Sanchez would be lacking the desire to perform and expressed his belief the forward would stay with the club beyond the January window.
"You say everybody thinks City will come in for Alexis – I am part of everybody and I don't think he will go," Wenger said.
"Do City need him? They have to decide that. But we need him here.
"I expect him to be motivated against City but that is always the case. One thing you cannot fault in Alexis Sanchez is his motivation. When he plays for Chile, he plays with passion that is in South America.
"It's the same for [previous club] Barcelona and Arsenal. He is happy when he is on the pitch and that is all he wants.
"Was he close to joining City? No. But at the end of the day, close or not does not matter. It does not have any influence. What is important is that, when you are somewhere and you have the opportunity to give your best, that is what you must do."
When asked if he thought Sanchez would sign a fresh Arsenal deal, Wenger avoided the subject, replying: "Before Sunday, certainly not."