The Frenchman has, so far, refused to sign a new contract with the Ligue 1 giants, and most certainly looks to be on his way out of the club, either this summer, or on a free transfer next year.
Madrid's initial bid for the 22-year-old was turned down by PSG, but they submitted an improved one that is reportedly still being considered by Mauricio Pochettino's side. Carvajal is hopeful Los Blancos can bring Mbappe over to help them in regaining the LaLiga title.
"Hopefully Mbappe can join us before the window closes, he's a great player and would be some reinforcement," the right-back said.
Along with Carvajal, Madrid director Emilio Butragueno and coach Carlo Ancelotti also spoke out on the Mbappe situation, although both men preferred not to directly address the situation.
"We understand that the fans are expectant, all the media are talking about it, but we have nothing to say," Butragueno stated.
Ancelotti added: "Let's talk about the game, the rest is an issue for the club."
Brazilian midfielder Casemiro added that Mbappe is "a player of great quality", but said he preferred not to speak about a footballer who still belongs to PSG. "We must not talk about a player who is not here like us, he is a high quality player but he is not from Real Madrid," he said.