Mbappe is believed to be on the wishlist of almost every major club in European football, with Real Madrid, Manchester United, Paris Saint-Germain and Arsenal just four of the teams that have been linked with a move.
The France international scored 26 times in all competitions for Monaco last season, but Trezeguet, who represented the likes of Monaco and Juventus during a glittering career, has urged the teenager to continue his development at Stade Louis II.
"In the semi-final, we played Monaco with Juventus, and we knew he is a player with a great future and that's the most important thing," Trezeguet told reporters.
"He is aware of his qualities, he is aware he is just 18 years old so he has a good opportunity at Monaco because it is a beautiful city, and a world-class academy. But everything goes fast in football. Monaco has known a special case with Anthony Martial going to Manchester [United].
"Of course, the economic part is important but I think with time things happen naturally. I think he still has to prove his qualities with Monaco, even if he will have the last word."
Trezeguet spent five years with Monaco between 1995 and 2000 - scoring 52 times in 93 league appearances - before joining Juventus, where he spent 10 years.