But the Champions League finalists is expected to wrap the signing of the Brazil international, 24, on July 1, for the above fee.
A further £4m (5m euros) could be added in performance-related bonus payments and Fabinho’s arrival will likely be followed by the departure of Emre Can.
Fabinho has spent spells playing as a right-back but has excelled in defensive midfield and is viewed as a replacement for Can, who is out of contract this summer and has repeatedly been linked with Juventus.
The Brazilian, whose deal will begin on 1 July, said the club’s infrastructure looked “exceptional”.
“I am really excited about this move,” Fabinho told Liverpool’s website. “This is something that I always wanted — this is a giant of a team. The infrastructures of the club look exceptional.
“A football club of this size coming after my services, I didn’t have to think that much about coming over.
“I will try to create my own history at this football club. Hopefully, on a personal level, I’m able to win titles with this club. I will try to grow and learn and improve myself, and to be part of the club’s history. Fabinho, who joined Monaco on loan from Portuguese side Rio Ave in 2013, won the French league title in 2016-17.
Fabinho, capped four times by Brazil but not part of their World Cup squad, has made 232 appearances for Monaco over five seasons, scoring 31 times mainly from his anchoring midfield position.