The 18-year-old, valued at a colossal 180 million euros by the Ligue 1 champions, is reportedly a target for Spanish giants Real Madrid and Premier League club Manchester City.
"We are holding talks on an extension with Kylian. I hope that we will get there," Vadim Vasilyev said on Monaco's Twitter page on Wednesday.
Vasilyev said there had been offers, though.
"We've had some major offers for Mbappe. He's the biggest hope in world football."
Last week Monaco said a number of "important" European clubs had approached Mbappe without their permission, breaking French league rules and FIFA statutes.
Mbappe is seen as one of the most exciting prospects in world football, scoring 26 goals in all competitions last season and helping Monaco win the league and reach the semi-finals of the Champions League.
(Reporting by Martyn Herman; Editing by Hugh Lawson)
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