Arsenal Wenger confirmed the news as his ended their tour of Australia with a 3-1 win over Western Sydney Wanderers.
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 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.
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