There is the risk for Liverpool that it could prompt other suitors to move in for him as well, hence why they are looking to complete a deal before the tournament kicks off June 14.
The 24-year-old will replace Emre Can, who looks set to join Italian champions Juventus when his contract at Liverpool expires at the end of next month.
Speaking to Liverpool.com, Fabinho said, "I believe I am a player that can organise the game well for my team".
He has made more than 200 appearances for the club in all competitions and played a key role in their triumphant 2016/17 Ligue 1 campaign.
"It's been a few years of him demonstrating his quality".
"He is also very good for someone who comes to a new country, a new city - someone who speaks the same language".
But Fekir played down his comments, and said: "If Fabinho is to be my future team-mate?"
Lewis Hamilton expects Daniel Ricciardo to stay at Red Bull
More so because of the nature of Monaco, where overtaking is next to impossible. "He was stronger there and I couldn't follow". Were Ferrari attempting to use Raikkonen as a pawn to aid Vettel's race yet again? Max Verstappen (NED/Red Bull) 25.317, 10.
The French worldwide made "it clear [to Aulas] he wants a move to Anfield and would like his future decided before the World Cup starts".
PARIS-Olivier Giroud and Nabil Fekir were on target as France stepped up their World Cup preparations by beating the Republic of Ireland 2-0 in Paris on Monday evening. Liverpool paid £39 million, according to reports from BBC Sport, for the versatile midfielder, which is a price that suggests he has been signed for the starting eleven.
Fabinho has scored 29 goals in his three seasons in Monaco despite being a holding midfielder. No benefit for Lyon to do anything before.
The group look delighted as they toast Fabinho's move in a glamorous fashion - on a private jet en route to Liverpool's Melwood training complex.
Lemar, 22, wasn't at his best last season, but he has shown throughout his career already he is capable of opening a match up in the final third.
If Liverpool can add these Ligue 1 gems to their squad ahead of next season, they would be sending out a significant statement of intent to the rest of European football.