The noises from Lyon suggest that they'll wait until after the World Cup before discussing the possible sale of their captain, but Liverpool are hoping to get business done early this summer and will be hoping to get a deal done well before the tournament kicks off.
Fabinho began his professional career in Portugal with Rio Ave. "Real choices, not just interests". Interestingly, the move was pushed through by his agency Gestifute who are owned by renowned "super agent" Jorge Mendes.
"If Fabinho is to be my future team-mate?"
Fabinho actually had a quieter season this time around.
"I am really excited about this move", Fabinho told Liverpool's official website.
Fabinho become the first new arrival at Liverpool this summer on Monday.
"He is a very good player, of global level", Fabinho said.
Georginio Wijnaldum has been one of Liverpool's most underappreciated players but his role going forward is also uncertain.
And Fabinho believes he will also adapt, adding, "I believe I am a player that can organise the game well for my team".
He started out as a right back, until he was converted to a centre midfielder with the French club.
Fabinho was a virtual ever-present in Monaco's engine room during their victorious Ligue 1 campaign, forming an excellent partnership with Tiemoue Bakayoko, now of Chelsea.
Crucially, Klopp has made efforts to remedy key areas and improve their strength in depth with signings that not only upgrade on their existing personnel, but offer a means of tactical flexibility..
Despite the fact that Fabinho has been playing at an arguably higher level in France compared to Ukraine, some United fans have already taken to Twitter to lambast Liverpool's latest transfer dealing due to his omission from the Brazilian squad. He ranked among the top three tacklers in France this past season and is also among the top six for total passes too.
What will Liverpool's midfield look like next season?
The Anfield outfit stole a march on their Premier League rivals by announcing the signing of the versatile Brazil global last night, despite the 24-year-old having been heavily linked with Manchester United and PSG for the last 18 months. He has even played in a Champions League semi-final as his Monaco side were beaten by eventual runners-up Juventus 6-1 on aggregate in 2017.
Another string to Fabinho's bow is that he is an excellent penalty taker.