PSG travel to Madrid on February 14 for the first leg of their last 16 tie as they look to end the Spanish side's two-year reign as European champions.
Having crashed out at the same stage of the competition last term, the French side are determined to prove themselves as a main challenger for the title this year.
"We are the two best teams in the world. Well, Real Madrid are the best team in the world, as they've won two consecutive Champions League titles, while we are growing," he told Marca.
"I think it'll be a great knockout tie and we will go to the Estadio Santiago Bernabeu to qualify.
"It's special because it's the last 16, a very important game. We know that we can prove a point to the world. It's a game that can go down in our history against the reigning champions and we are all very motivated.
"You have to respect every team, but when we get to the Bernabeu we will give the utmost respect. We have to show our quality.
"Above all, that they are very complete. They have some of the world's best in every position and they have played together for years."
With €222 million signing Neymar and Mbappe, whose loan from Monaco will be made permanent at the end of the season for around €180m, teaming up with Edinson Cavani at Parc des Princes this term, the 19-year-old is sure they can go all the way.
"We don't think about being the best attack in the world, only the best team in the world," he added. "What we want to do is win and be competitive, it's good that we are the best attack in the world, but it doesn't guarantee you anything, it's the whole team that wins. It's true that it's good to have a good striker, but you have to win.
"We had a great group stage and we have the opportunity to show the world that we can knock out the team that has been champion of Europe in the past two seasons. So there's no pressure, not at all, the pressure isn't on us. We are going to play our game, our style and give our all to qualify."
The competition for European football's most prestigious title is intense, however, and Mbappe knows that beating Madrid will not give them a straight path to the trophy.
"Madrid have dominated football in the past few years, but I think that it's not just them, there are other great teams. There's Manchester City, who are very powerful now. We are there, as well as Juventus and Bayern Munich. There are a lot of teams who could go far."
"Without a doubt. The winning team from this last 16 tie will be the favourite to win the Champions league. If we can beat Real Madrid, the other teams will be scared. If Real Madrid do it, the same. Whoever wins, from then on, will be terrifying for the rest."