Several newspapers reported on Friday that the Germany international had told his Gunners teammates that he will be moving to Old Trafford when the transfer window reopens.
Ozil's contract expires in the summer, leaving the £42.5m signing from Real Madrid facing a potential move away from the Emirates Stadium for a cut-price fee.
"We have to deal with all kinds of speculation when the players are at the end of their contracts," Wenger told the official Arsenal site.
"On the other hand, to be professional is to give 100% as long as you are somewhere. For the rest, we came out many times and said that's the situation.
"[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%.
"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."
Arsenal, currently sixth in the Premier League table, next face Everton away on Sunday.