The Reds signed the Brail international in a £39m deal from Ligue 1 side AS Monaco last week to bolster Jurgen Klopp’s midfield.
Liverpool FC were short on options in the middle of the park for their 3-1 loss to La Liga side Real Madrid in the Champions League final in Kiev.
Alex Oxlade-Chamberlain is currently sidelined with a serious knee problem that he suffered in a 5-2 win over AS Roma in the first leg of their Champions League semi-final.
Germany international Emre Can has been linked with a potential move to Serie A champions Juventus as the versatile midfielder’s contract will expire this summer.
Fabinho won the Ligue 1 title in the 2016-17 season and helped AS Monaco to reach the Champions League finals before a loss to Juventus in the last four,
Former Liverpool FC defender Nicol welcomed Fabinho’s addition to the Reds team in the summer transfer window.
“He isn’t stuck in one position,” Nicol told ESPN FC.
“He is a football player. Klopp likes players he can move around and still can do as good a job wherever you put them.”
Liverpool FC signed Netherlands international Virgil van Dijk in a £75m deal from Premier League rivals Southampton in the January transfer window.
The Reds finished in fourth place in the Premier League table to secure Champions League football in consecutive seasons.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news