And the Liverpool midfielder could follow teammate Jordan Henderson to the Gulf nation, with the Reds skipper a target for Steven Gerrard's Al Ettifaq.
Saudi sides have dominated the summer transfer window so far, with a number of high-profile players swapping Europe for the Middle East.
Al Ittihad have been one of the biggest movers so far, bringing in French pair Benzema and Kante on free transfers, while splashing out £25m to sign winger Jota from Celtic.
And they have now identified their next possible recruit, with The Athletic reporting they will make a £40m proposal to Liverpool for Fabinho.
It remains to be seen whether Fabinho, who still has three years left to run on his contract at Anfield, would entertain a switch to Saudi Arabia.
READ MORE ON LIVERPOOL
Henderson left teammates visibly stunned at his physique on return to training
I could've signed Van Dijk for £6m but was advised not to proceed with transfer
But you can be sure Fabinho would be in line to receive a monster salary, with Henderson claimed to have a £700,000-a-week deal on the table - almost four times his current pay packet in Merseyside.
The news outlet has also stated that Liverpool are hesitant at allowing the 29-year-old to depart without finding a suitable replacement.
Southampton's Romeo Lavia is on Liverpool's radar, but they have yet to turn their interest into a formal bid.
Fabinho has been a mainstay in Klopp's line-up since he joined from Monaco in 2018, where he has featured in 219 games in all competitions.
Most read in Football
Man United transfer news LIVE: Hojlund part-exchange offer made, Onana talks continue
Arsenal transfer news LIVE: 'Official' Timber photos leak, Rice deal further delayed
Alli reveals childhood trauma, Henderson considers Saudi offer, Rice delay angers West Ham
Alli reveals Kane and Dier intervened and Everton stood by him through rehab for addiction
Should Fabinho and Henderson depart, Liverpool would have seen seven midfielders shipped out this summer.
James Milner, Naby Keita and Alex Oxlade-Chamberlain were all released, while Fabio Carvalho was loaned out to German side RB Leipzig.
And Liverpool also failed to turn Arthur Melo's temporary stay from Juventus into a permanent deal.
Only two midfielders have been signed by Liverpool this window - Alexis Mac Allister from Brighton and Dominik Szoboszlai from Leipzig.