Mbappe represented Monaco between 2013 and 2017 before joining PSG on a season-long loan.
The Frenchman then completed a permanent switch to the capital club in the summer of 2018 and has continued his excellent scoring form for the club, now managing 70 goals in 100 appearances in all competitions.
Madrid continue to be strongly linked with a swoop for the 20-year-old, though, and Vasilyev expects the Spanish giants to eventually secure a move for the 2018 World Cup winner.
"Kylian will join Real Madrid, I do not know when, but it seems inevitable," Vasilyev told Le Parisien. "The club is very important in his life. Madrid had a more interesting offer than PSG in 2017 but he told me he that thought it was too early to leave France, and Paris was his home.
"He wanted to become a great player in France as he would have plenty of time and that showed Kylian's intelligence - he is now the best player in France and PSG have enough finances to keep him."
Mbappe scored his 10th goal of the season in PSG's 2-2 draw at the Bernabeu in the Champions League on Tuesday night.