Mbappe was recently named as the new captain of Les Bleus and marked his first official game as France's new leader with two goals and an assist in a 4-0 win over the Netherlands on Friday.
That brace took Mbappe to 38 goals in 67 appearances for his country.
Only four players have scored more than Mbappe in the history of the France national team, with Platini next in line on 41 goals.
Antoine Griezmann(43), Thierry Henry(51) and Olivier Giroud(53) complete the top three.
Mbappe can draw closer to Platini when France play the Republic of Ireland in a EURO 2024 qualifier on Monday.
He said at Sunday's pre-match press conference: "It's an honour but it's also the next target to beat.
"Platini remains a legend of French football but I want to continue my journey and it goes through Michel Platini."
Elaborating on his maiden game as France captain, Mbappe continued: "I was the same, I naturally played my new role. There was not much to say in relation to the team's performance. I'm not going to talk just to talk.
"I was the link between the two generations but there were no differences during the week. The group is doing very well, I did not have to intervene. The less work I have, the better for everyone.
"We must not get carried away and we have started qualifying well. Tomorrow's match will be more complicated than what people may think."
