Saka is proving to be one of the best young players at this year's tournament, having struck three times already in England's four games.
Mbappe was the biggest breakout star at Russia 2018 when he was named young player of the tournament and scored four goals, including one in the final against Croatia.
Mbappe has continued from where he left off in Russia in Qatar, scoring five goals to lead the goalking charts.
The two young talents will go head-to-head on Saturday when England face France in the World Cup quarterfinals but Saka says he cannot be compared to the Paris Saint Germain superstar.
Asked whether he could follow in Mbappe's footsteps by being named young player of the tournament, Saka said: "Thank you for the compliment, but there's only one Kylian Mbappe.
"At the same time, there's only one of me. I just want to be myself and help my team in the best way I can.
"There are many young players in this tournament, I can name so many.
"Even in our team, alongside me there's another young player doing unbelievably well in Jude Bellingham. I'm just happy that we're all here and doing well.
"The priority is to try to win the tournament, rather than to be the player of the tournament or young player of the tournament."
Asked about Bellingham's displays in the England midfield, Saka added: "He's a special player. I don't really know the words to describe him.
"I just hope he can continue to keep progressing because, for sure, he has a massive, massive future."
