The Spaniard has been with the Red and Whites since 2019, featuring on 150 occasions for the club, and he has another four years left to run on his contract at Wanda Metropolitano.
However, according to The Athletic, Al-Ahli are now in a strong position to complete a £20m move for the 28-year-old during the current transfer window.
Edouard Mendy, Roberto Firmino, Riyad Mahrez and Allan Saint-Maximin have already made the move to Al-Ahli this summer, with the club building a star-studded team for the new campaign.
Llorente missed the end of last season through injury, and he was restricted to only 29 appearances for the Red and Whites in 2022-23, scoring three times and registering three assists in the process.
Staying with Saudi Arabia, Al Shabab have allegedly been in touch with Fulham attacker Willian to discuss a possible move to the club this summer.
The Brazilian only recently penned a new contract at Fulham, turning down interest from Nottingham Forest to re-sign for Marco Silva's team until next June.
However, according to transfer expert Fabrizio Romano, Al Shabab have a 'concrete interest' in the 34-year-old, who scored five Premier League goals during the 2022-23 campaign.
Willian's agent is allegedly holding talks with the Saudi outfit over a possible transfer.
Al Shabab finished fourth in the Saudi Pro League last season, picking up 56 points from their 30 matches courtesy of a record of 17 wins, five draws and eight defeats.
Meanwhile, according to SPORT, Manchester United have put an asking price of £6m on Matej Kovar amid the speculation surrounding the goalkeeper's future.
The 23-year-old has been with the Red Devils since 2018 but is yet to make a first-team appearance.
Kovar spent time out on loan with Swindon Town and Burton Albion in League One in 2020-21 and 2021-22 respectively, before enjoying a successful spell with Sparta Prague last term.
The goalkeeper's form for Sparta is believed to have attracted a host of attention, with Aston Villa said to be showing an interest in his services.
Spanish outfit Cadiz are also said to be keen on a player who will cost in the region of £6m.
Kovar has been involved in Man United's preparations for the new season, featuring in the friendlies with Leeds United and Lyon earlier this summer.