The duo, whose contracts expire at the end of the season, are being strongly linked with moves away from the Emirates Stadium.
Alexis, 28, continues to be linked with Man City despite missing out on a move to the Etihad Stadium last summer, while Ozil, 29, is reportedly attracting interest from Man Utd and Barcelona.
But speaking to the media ahead of Arsenal's Premier League clash against Huddersfield on Wednesday, Wenger has ruled out selling the pair in the winter transfer window.
When asked whether Alexis and Ozil would remain at Arsenal beyond the January window, Wenger replied: “Yes, of course.
"No doubt. I don't think every day about that at the moment. As long as they are here, they give their best for the club.
“As far as I'm concerned, they'll stay until the end of the season unless something unbelievable happens.
"In press conferences, you confront me with speculation, but for me they stay until the end of the season - that's what we decided at the start of the season.”
Arsenal run the risk of losing Alexis and Ozil for nothing at the end of the 2017-18 season as negotiations over contract extensions at the club continue to stall.
When asked about whether Arsenal could still tie down the pair to fresh terms, Wenger added: "Will they stay longer? That's impossible to say right now, but they have a contract until the end of the season.
"If it's up to me then, yes, they stay next season. But there's more to it than that. They have to decide that."
Arsenal are looking to make it three league wins on the spin when they host Huddersfield on Wednesday.