Fabinho, 24, played 45 games for Monaco this season as they finished second in Ligue 1 behind PSG.
He will bolster Jurgen Klopp’s central-midfield ranks, with Liverpool seeing him as the ideal replacement for Emre Can.
Germany international Can is set to leave the club with his contract due to expire next month and Juventus is his expected destination.
Fabinho boasts a handful of caps for Brazil (Image: GETTY)
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The Reds have been working quietly on a deal for Fabinho, who also attracted interest from Atletico Madrid, Paris Saint-Germain and Manchester United.
Monaco had strived to keep their star man, knowing Thomas Lemar could also leave the club if a sizeable offer comes in.
They also lost Kylian Mbappe, Tiemoue Bakayoko, Benjamin Mendy and Guido Carrillo last summer.