The 18-year-old has been heavily linked with the European champions amid a breakout second season at Stade Louis II.
Madrid head coach Zinedine Zidane, Mbappe's countryman, is known to be an admirer of the teenager, having sought, without success, to sign him for the club's youth academy in 2013.
President Florentino Perez has also expressed his tentative interest in pairing Mbappe with fellow Frenchman Karim Benzema up front at the Santiago Bernabeu.
And Ramos this week stated Madrid's doors are "always open for the best players" when asked about the exciting forward.
"Real Madrid? For now, I am in Monaco," Mbappe said.
"Then we'll see what happens. Real Madrid is a very big club, yes. But I think I still have a lot to learn.
"Real Madrid is a club where you have to go when you are mature and at the top of your game.
"I do not think I'm at the top of my game right now."
Ramos also spoke to journalists following his team's victory at Stade de France, highlighting the potential value of the Ligue 1 newcomer's pace.
"Mbappe is a young player who brings a lot of speed, especially on the counter, which is decisive," he said.
"I wish the best to this boy. Today, Real Madrid has very good players. Recruitment does not depend on me, as I have already said. But it is obvious that Real Madrid always has the doors open for good players."