The 18-year-old forward had been linked with Real Madrid, Paris Saint-Germain, Manchester City and Arsenal after he helped Monaco to the Ligue 1 title last season.
Local media reported that Arsenal had made a bid of 123 million pounds for Mbappe, but Wenger denied that after his side beat Western Sydney with goals from Olivier Giroud, Aaron Ramsey and Mohamed Elneny in front of 84,000 at the Olympic Stadium on Saturday.
"That's not true," Wenger told the club website (www.arsenalfc.com) after the match. "People have a big imagination.
"What we know now about Mbappe is that it's over 100 million. After that it's free to imagine what you want.
"But we have not made an offer.
"It looks like he will stay at Monaco. Too much choice maybe, so in the end people don't move."
Wenger added that Chilean forward Alexis Sanchez had not agreed a new contract with the club, despite both the manager and his fellow players wanting him to stay.
"No, a lot that comes out (about) Alexis doesn't look completely right," Wenger said when asked if the Chilean had agreed a new contract. "No, that's not the case."
The 28-year-old has one year left on his contract and British media have reported he is the target of Manchester City.
Sanchez then suggested later that he was no closer to signing a new contract with Arsenal when he said at a charity game in his home town of Tocopilla that he wanted to play in the Champions League.
Arsenal did not qualify for next season's Champions League for the first time in 20 years, after finishing fifth in the English Premier League.
The victory over a physical Western Sydney follows a 2-0 win over Sydney FC on Thursday and sets Arsenal up for their matches against Bayern Munich in Shanghai on July 19 and Chelsea in Beijing on July 22 as part of the International Champions Cup.
"It will be less robust physically but of course you play against teams who have top quality going forward," Wenger said of what he expected against the European clubs.
"In the last two games we focussed a lot on attacking ... Apart from that we will play in a different climate. It will be very hot, so we have to adapt to that as well."
(Reporting by Greg Stutchbury in Wellington; Editing by Andrew Both)
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