Sanchez has been tracked by Manchester City, his preferred destination, with a move to Paris Saint-Germain now looking less likely.
The Chilean has been ruled out of the Gunners' big kick-off against Leicester City this Friday at the Emirates Stadium, and the trip to Stoke next Saturday.
But the Gunners boss has also publicly stated he remains confident both Ozil and Sanchez will remain at Arsenal for the upcoming season.
Asked if any bids had been lodged for Sanchez, the Frenchman replied: "I can't tell you that at the moment".
Arsenal offer Alexis Sanchez mammoth £300000-a-week contract
Arsenal have signed two players so far this summer as they prepare to try and challenge for the Premier League title this season. Arsenal boss Arsene Wenger admits that he is "not super optimistic" about Alexis Sanchez's contract situation.
But Wenger said he had not heard from PSG president Nasser Al-Khelaifi and referred to French media reports suggesting PSG are more interested in signing Monaco's Kylian Mbappe.
Shakespeare: 'If you look at the third goal, I am a bit disappointed with the handball leading up to it, but you have to defend the corner better.
Arsenal would let Sanchez go to PSG tomorrow.
Arsenal's first five Premier League fixtures are against Leicester, Stoke, Liverpool, Bournemouth and Chelsea. "I don't think I would have included him certainly on Friday night - I don't think I would have started him".
'Some players rush into deals because they think they have to go to avoid getting found out.
Arsenal attacking midfielder Mesut Ozil will sign a new contract that will see him earn more than £220,000 per week. 'I have sympathy for him.