Fabinho moved to Liverpool from French side Monaco in a £43.7 million ($57 million) deal earlier in the close-season and the Brazilian is confident of a memorable first season on Merseyside.
Two of Fabinho's former Monaco colleagues, Benjamin Mendy and Bernardo Silva, play for Premier League champions City.
Liverpool finished 25 points behind City in fourth place last term.
But Fabinho is sure Liverpool, who reached the Champions League final last season, are in good shape to win the club's first English title since 1990.
Jurgen Klopp's squad has been bolstered by the recent arrivals of Fabinho, Naby Keita, Xherdan Shaqiri and Alisson.
"I believe we have a very good team and we will be able to fight for the title," Fabinho was quoted as saying by the British media.
"I understand we have excellent players. We have an excellent manager. 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."
If Liverpool could win the title, it might help Fabinho's cause as he attempts to persuade his friend Mbappe to swap Paris Saint Germain for the Reds.
Fabinho and Mbappe played together at Monaco, helping them to win the Ligue 1 title in 2016-17.
Mbappe then moved to PSG and won the domestic treble last season before lifting the World Cup with France earlier this month.
He scored four times in Russia, winning the best young player award after emerging as the sensation of the tournament.
When asked about the 19-year-old forward, 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."
Asked if he would tell Mbappe to come to Liverpool in the future, 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."