Fabinho swapped Monaco for Merseyside in a £40m deal earlier this summer, kicking off a series of high-profile signings which has since seen Liverpool sign Naby Keita, Xherdan Shaqiri and Alisson Becker.
The 24-year-old Brazil international has now revealed that former Monaco teammate Mbappe congratulated him on the move, and joked that he will try to persuade the World Cup-winning 19-year-old to also join Liverpool.
"Kylian sent me a text message congratulating me on going to Liverpool," Fabinho is quoted as saying by The Telegraph.
"I have not had the chance to congratulate him yet on what he did winning the World Cup. What France did was fantastic. What Mbappe did in two years of professional football is amazing. He is a phenomenon and needs to be congratulated. As soon as I have the chance I will.
"He has already said for the next season he will remain at PSG, but I will try slowly to convince him to come to Liverpool."