With Neymar having struggled with injuries during his time in Paris, Mbappe has often established himself as the key player in PSG's attack since his move from Monaco in 2017.
The 21-year-old scored 39 goals across all competitions last season and already has 18 to his name this campaign.
However, Mbappe insists he is not wishing to take any limelight away from Neymar, who has been in fine form for Thomas Tuchel's side when fit this season.
"When I arrived in Paris, there was no debate. It was him [Neymar], the superstar, whom I had come to help a little," Mbappe told France Football.
"He gets injured, [Brazil go out of] the World Cup and I win it. And there begins to come out stories about our alleged rivalry, about my willingness to take his place.
"I was shocked to hear all of this. When I came back in August 2018, the first thing I did was go and catch Neymar to tell him: 'Don't worry, I won't be walking on your flower beds here. I assure you that I do not want to take your place, you can keep it. I'm always here to help you.'"
Mbappe may not be aiming to compete with Neymar, but he is looking to get the better of another superstar.
Lionel Messi won a record sixth Ballon d'Or this year, and Mbappe has set his sights on finishing as the top scorer in Europe, though he acknowledged it will be tough to outdo the Barcelona forward.
"Rather than putting my head down and waiting quietly for the end of the season, I tried to outdo myself," Mbappe said.
"I then realised that I could try to seek this title of best European scorer. But, opposite, there was Messi. I'd score two, he'd score three; I'd score three, he'd score four!
"It was so crazy that I talked about it with Ousmane [Dembele]. 'It is not possible, does he do it on purpose? He looks at the number of goals I score?' 'Of course he's looking at you!'
"I said to myself: Yes, Messi is watching me. It is flattering to see that such a player does not neglect you."