The Brazilian midfielder turned defender is set to make his 100th for the club against West Brom on Sunday.
The Reds ended a 30-year wait to be crowned champions of England in July with a whopping 18-point advantage over Manchester City.
Liverpool have made light of injury problems this season to hold a four-point lead over Christmas in the chase for successive titles.
“This team will be remembered for how well we play, the quality of our football and for winning the title,” Fabinho said in an interview with the Daily Mail.
“But to fight for the second one would put us further in to football history. It would put us up there with teams in the Premier League that have won back to back titles. Teams like Manchester City.
“It would put us on the higher level and put us with the best teams in the history of the league.
“Taking into account everything that has happened this year, the difficulties of no fans in the stadiums and the busy run of fixtures and injuries we have had, it all adds to making the second title more special than the first one if we could do it.
To fight for the second one would put us further in to football history. It would put us up there with teams in the Premier League that have won back to back titles.
Liverpool midfielder Fabinho
“It would show that we have this constant desire at the club to be winners.”
Long-term injuries to Virgil Van Dijk and Joe Gomez has forced the Brazilian midfielder to drop deeper into central defence.
Yet the 27-year-old has hardly put a foot wrong since Liverpool’s last domestic defeat, the 7-2 horror show away to Aston Villa at the start of October.
Fabinho said that plans for him to play at the back had been in operation almost from the day he arrived at Liverpool in July 2018.
“Back then the coach saw the need for someone to be available so I started working on that position, getting used to it, working with potential partners,” said Fabinho, who is set to make his 100th Liverpool appearance against West Brom on Sunday.
“We had three centre-backs at the time so it was all just a test for me, just to be prepared. The coach had identified that there could be a need further down the line.
“So when I came in I felt good and comfortable and over time it’s got easier.
“When Virgil got injured I expected to come in as centre-back and even the other players were joking. They were saying: ‘Fabinho the defender is back, he is here’.
“Yes I was nervous at first but I think I have grown in to it.”