Mbappe burst onto the scene four years ago in Russia, winning the FIFA Young Player of the Tournament award as he scored four goals on the way to France securing the trophy, also becoming only the second teenager ever to score in a World Cup final after Pele.
Asked at a news conference on Monday if Saka felt he could make a similar impact at these finals, the England forward said: "Thank you for the compliment but no. There's only one Kylian Mbappe.
"At the same time, there's only one me. I want to be myself and help the team in the best way I can.
"There are so many young players in the tournament, I can name so many. Even in our team, there's a young player who's doing unbelievably well in Jude Bellingham.
"I'm just happy we are all here and doing well. The priority is to win the tournament, not be player or young player of the tournament."
Meanwhile, the Arsenal winger vowed to step up and take a penalty if required against France.
And looking ahead to Saturday's game at Al Bayt Stadium, Saka said: "I've matured and progressed a lot as a player and a person since that moment [against Italy].
"I wouldn't have stepped up the times I have stepped up for Arsenal to take a penalty if I wasn't confident so if the moment comes and I am selected to take it, I will be more than happy to.
"To be honest, I feel like personally I've tried to move on from that moment. Obviously I know I can never really forget about it, it is going to be in history. But at the same time, coming out here and scoring those three goals, of course lifted me a lot.
"Like I keep saying, the love from the fans that I keep receiving lifts me a lot as well. It gives me a lot of confidence and I love to see that from the fans."
England are the tournament's top scorers having netted 12 times, but they now face a significant step up against defending champions France, for whom Mbappe has already scored five times in four matches.
"There's no doubt the quality we have in our team," Saka added. "We are blessed with an amazing front line, we have so many quality attacking players and when you get selected in that lineup it shows how much confidence and trust the coach puts in you so it gives you that extra confidence to go out there, shine and last night we were able to do that.
"I'm not a manager, I'm a player. I have to trust Gareth and our coaching staff to prepare the best gameplan but I think we can continue to do what we're doing. We've been playing well and score the most goals in the tournament do I don't see us needing to change too much."