It was reported this morning that the Germany international had told his Arsenal team-mates that he will be moving to Old Trafford in the January transfer window.
Ozil has endured a difficult season with the Gunners so far in what is likely to be his final year with the club, with his contract expiring at the end of the season.
That situation means that Ozil, who joined from Real Madrid four years ago in a deal worth £42.5m, could leave the Emirates for a cut-price fee in January.
However, Wenger has faith in the 29-year-old midfielder's conduct and told the club's website: "We have to deal with all kinds of speculation when the players are at the end of their contracts.
"On the other hand, to be professional is to give 100 per cent as long as you are somewhere. For the rest, we came out many times and said that's the situation.
"It [the media] can come out tomorrow and say that he extends his contract here. It will be exactly the same, it will not change anything. When you play the next game, commit 100 per cent.
"When a player plays for Arsenal Football Club, his commitment cannot be linked with the length of his contract, it has just to be linked with the responsibility and the ambition he has to win the football game."