Mbappe, 18, has been the subject of one of the biggest transfer sagas of the summer with Real Madrid and Manchester City both linked heavily to the teenager.
Various reports have suggested that an agreement was close to being reached with a fee of £161 million possibly on the table in order to sign the forward after his stellar debut season.
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However Vasilyev held a press conference on Wednesday where he dismissed such claims.
“I assure you there is no agreement with a club,” Vasilyev said.
“We have very great demand for Mbappe. He’s the biggest prospect in world football.
“We are discussing an extension with Kylian. I hope we’ll get there.”
Vasilyev also discussed Brazilian forward Neymar, with the Barcelona man linked with a move to Ligue 1 title rivals PSG.
“I think it would be a good think for Neymar to play in Ligue 1. It would be good for France.”
He also added that he felt it would be difficult for Monaco to defend their title this year.
"it will be difficult to defend the title. We know who will be the favourites but we are ambitious.”
He added later on that he expects both Thomas Lemar, who had been linked to Arsenal, and Fabinho to stay.
"We have kept all of the key players that we intended to keep… I will address speculation relating to the case of (Thomas) Lemar. He is staying with us. He is an immense talent and is essential for the team.
"Fabinho stays, he is an essential player in the midfield.”
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