In an interview with French newspaper L’Equipe, Eto’o heaped praise on the France and PSG forward.
The ex-Barcelona forward hopes he gets the opportunity to speak to the teenager, who he believes can become the game’s next superstar.
"If he manages himself well, if he understands what is going on around him, he is the future Messi," said the Cameroonian, who is still playing professional football, now in Turkey.
"There are so many things to bear in mind if you want to have a great career which are separate from a player’s’ qualities, even if he is abnormally good. I hope I have the opportunity to speak with him one day," added Eto’o.
"Kylian can inspire himself on the super-human mental strength that Leo Messi has.
I saw him (Messi) grow up at Barça. He makes games look easy by creating things every second. He is unique, but he is still like the small child I saw in 2004, discreet, quiet. Others might have gone crazy in face of world wide glory."
The Cameroon international forward turned out with the Argentine at Camp Nou from 2004 until 2009 and saw at first hand the talents that carried him to five Ballons d’Or.
Mbappe burst onto the scene with Monaco last season, helping them to win Ligue 1 and reach the Champions League semi-finals before making the move to his hometown club in the summer.