Arsenal have offered Alexis Sanchez a new contract worth £300,000 per week.
The Chilean global suffered the injury in training on Sunday morning and will now miss our first two games against Leicester and Stoke while he could also be a doubt to face Liverpool at the end of the month.
Wenger has revealed how uncertainty over his future last season created a "lack of clarity in the dressing room" and saw players asking him what was going on.
Sanchez has been instrumental to Arsenal's fortunes ever since he joined them from Barcelona back in the summer of 2014.
The Chilean has so far resisted all attempts by Arsenal to extend his contract, and it remains to be seen if he will sign the new deal now on offer.
What an Arsenal fan reads: "Alexis Sanchez sticks two fingers up to the fans and runs off with his dogs as he waits for Chelsea/Man City/PSG move to be completed".
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Details of the bid for the forward are still unclear, although RMC Sport have claimed United have already rejected it. Manchester United turned down both approaches, considering him off the market.
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Wenger said Sanchez would be missed but admitted he would not have started the game against Leicester even if he was deemed fit to play.
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Wenger has conceded that Sanchez is not willing to prolong his stay at the Emirates meaning he is on course to walk away for free in a year's' time when he will be 29.
"He had a little abdominal strain that he caught on Sunday morning in training, before he came to Wembley", he said in his press conference before the opening Premier League game of the season.
When asked if Arsenal have received bids for Sanchez, Wenger replied: "I can not tell you that".
"But I think Ozil will get better and will take on centre stage for Arsenal this season". "When you are not completely in or the players feel you are not completely in, it is hard to tell them we go (out to win)".
Some may disagree with that sentiment and feel Arsenal could do with the addition of the 2015-16 PFA Players' Player of the Year, who has stood out as one of the Foxes' elite stars in recent years.
A poor start to the season has severely hampered Arsenal's ambitions over the past seven seasons, winning just once with three draws and as many defeats. 'I have sympathy for him.