The Frenchman has one year left on his contract at Tottenham but could be allowed to leave this summer after over a decade at the club.
Lloris is open to a new challenge and there is a firm offer from Saudi Arabia that would at least treble his £100,000-a-week contract, according to The Times.
It is the latest ploy from the Gulf state to bring in world-renowned talent having already signed Cristiano Ronaldo earlier this season.
There are further plots to bring in Lionel Messi, Sergio Busquets and Jordi Alba along too.
Ronaldo joined Al Nassr on a whopping £177million-a-year deal after his contract at Manchester United was ripped up.
And Al Hilal could sign Messi on a contract worth almost double that with his deal at Paris Saint-Germain set to expire at the end of the season.
The report adds that Lloris, who has made 447 appearances for Spurs, has other offers on the table but the one from Saudi Arabia is by far the most lucrative.
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However, the 36-year-old is yet to make a decision on his future and wants to talk to Tottenham chief Daniel Levy before anything else.
He wants to know who is arriving as the next manager and what direction the club is going after a disappointing season.
But Spurs are already in the market for a long-term replacement to Lloris, who no matter what will most likely leave either this year or the next.
The Times further report that three replacements have been identified.
Brentford's David Raya, Everton star Jordan Pickford and Brighton keeper Robert Sanchez have all been linked as potential signings this summer.
It means that Lloris might have already played his last game for the club having been ruled out for the rest of the season with a thigh injury.
His last appearance for Spurs was the gruelling 6-1 pummelling by Newcastle last month, where the London outfit conceded five after 21 minutes.
Lloris was brought off at half-time in that match with the subsequent injury that has ended his season.
But it would be a sorry end to an otherwise stellar career at Tottenham where he will no doubt go down as a club legend.
The former France international has the most appearances for the club for a non-Briton and has been captain since 2015.
If he does move to Saudi Arabia, it would be the latest power play from the Saudi Pro League, which has received government backing as they look to boost their footballing status.