The 18-year-old has taken Ligue 1 by storm this season firing in 10 goals in all competitions including another against Manchester City as Monaco stunned the Premier League side to grab a place in the Champions League quarter-finals.
Mbappe has caught the eye of a host of European heavyweights this term including United who had representatives at the Stade Louis II to run the rule over the young striker.
Ligue 1 leaders Monaco are bracing themselves for offers for Mbappe this summer but vice-president Vadim Vasilyev insists the club are under no pressure to sell after watching him continue his breakout season against City.
“Our intention is to keep Kylian Mbappe,” he said. “Mbappe is a product of our youth academy. He is our DNA. I am very proud.
“We have a real team. The first half was excellent – the sort of performance that the very top teams make.”
Meanwhile, Didier Deschamps has handed Mbappe his first call-up to the French national team ahead of the World Cup qualifier with Luxembourg and the friendly against Spain.
"Talent does not wait around for anything," he said on Thursday. "There have already been young players in the national team."
United are in the market for a forward this summer with Celtic's Moussa Dembele emerging as an option alongside long-term target Antoine Griezmann.