The 18-year-old, the youngest player in the top five European leagues to reach 14 league goals in the 21st century, has been linked by European media with a possible move to Juventus, Barcelona or Real Madrid.
Monaco vice-president Vadim Vasilyiev, however, is hoping Mbappe, who is also the first player to score in each of his first four knockout games in the Champions League, would stay at least one more season.
"Our intention is that he stays, we are going to do everything we can so that he can stay with us," the Russian said.
"I have not discussed with any club, because what the player wants is the priority."
French media have reported that Mbappe is keen to stay at the club for another season.
The forward became a regular starter in October when Argentine striker Guido Carrillo sustained an injury and since then there has been no stopping him.
"He reminds me of Neymar at a young age," said Real Madrid striker Karim Benzema of his compatriot.
Mbappe's pace, technical ability and cool head make him one of the most feared strikers in Europe.
To put his impact in context, at the same age, Arsenal great Thierry Henry scored three goals in the French top flight during the 1995-96 season with Monaco.
"He reminds me of Thierry Henry," said Argentine striker Delio Onnis, Monaco's record scorer with 223 goals between 1973-80.
On Wednesday, Mbappe was in devastating form again, beating St Etienne keeper Stephane Ruffier with a deft feint to put the hosts ahead in a 2-0 win at Louis-II stadium.
(Reporting by Julien Pretot; Editing by Toby Davis)
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