Fabinho was congratulated by Kylian Mbappe on his move to Liverpool this summer - and he says he will try to convince the teenage "phenomenon" to join the club himself.
Fabinho, signed from Monaco for a fee of up to €50million (Dh214.1m), and Mbappe played together for the French outfit, helping them to win the Ligue 1 title in 2016-17.
Mbappe then moved on to Paris Saint-Germain, who made him the second-most expensive footballer of all time, and won the domestic treble last term before lifting the World Cup with France this summer, with the tournament seeing him score four times and claim the best young player award.
When asked about the 19-year-old forward, Brazilian midfielder Fabinho said: "Kylian Mbappe sent me a text message congratulating me for coming to Liverpool.
"Unfortunately I have not had a chance to congratulate him for what he did during this 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, and as soon as I have the chance I will."
Fabinho was then asked if he would also ask Mbappe to come to Liverpool, and he said with a smile: "He has already said for this season he will remain at PSG, but I will try slowly to convince him to come over."
There are two of Fabinho's former Monaco colleagues at Premier League champions Manchester City in Benjamin Mendy and Bernardo Silva, and he says he has been in touch with them.
He has promised Silva he will be "a bit harsh on him" should they face each other.
Transfer window: How the Premier League top six are shaping up
And he feels Liverpool - who have also had Naby Keita, Xherdan Shaqiri and goalkeeper Alisson arrive since finishing 25 points behind City in fourth last term - can challenge for the league title this season.
"I believe so," he said. "I believe we have a very good team and we will be able to fight for the title.
"I understand we have excellent players. We have an excellent manager (Jurgen Klopp). I understand also that City are the champions and last season they produced excellent football.
"We will do our best to get the title from them and make everyone happy here."
Fabinho, who has been advised by compatriot Roberto Firmino with regard to which areas to live in, has four Brazil caps.
Having not been involved in the World Cup, he is hoping performances for Liverpool can lead to an international recall.
And while admitting he needs to adjust as the Reds play in a different way to what he is used to, he has declared his readiness to operate wherever Klopp wants him to.
The 24-year-old, who has played at right-back as well as in midfield, said: "He (Klopp) has already said he can use me in various positions.
"If they need a leg up front, I'm happy to go up there. If they need a leg behind, I'll assist behind."
Klopp said when Fabinho joined that it was "cool" that he could "play 'six', 'eight' and 'two'."
Speaking this week about the player, Klopp said: "You have seen it a little bit with Fabinho, that he needs to settle - he's a little bit too deep between the centre halves. We do it differently to Monaco.
"You can push him into position but because it's natural for him moments later he's again deep. That shows he needs time to adapt to different styles."