However, PSG have also maintained contact with 18-year-old Mbappe despite the recent signing of Neymar, which Wenger believes will put an end to the reported interest in the Chilean forward.
"I think if you read the French papers they are on Mbappe's case to finish their transfer market," he said at a press conference.
"That's what I read in the papers and on my side I had no contact at all with Paris Saint-Germain [about Sanchez]."
After confirming the ex-Barcelona star will miss Arsenal's Premier League opener against Leicester City, Wenger reiterated he is determined to keep Sanchez at the club and says the club will not be tempted into a late-window sale as they look to tie him to a new deal.
"It's always possible when players are in final year of contract [to renew]," the Frenchman added.
"We will try to extend the contract. There's no reason why we shouldn't do it but we are not there yet.
"I think we are not open to any offers anyway."