Modric was heavily linked with a move to the Saudi Pro League last year, and it is believed that he was offered a three-year deal worth in the region of €300m (£258m) to move to Al-Hilal.
The Croatia international ultimately signed a new one-year deal at Real Madrid, and he has again been an important player for Carlo Ancelotti's side this season, making 22 appearances, scoring once and providing five assists.
Modric struggled for starts earlier this season when Ancelotti had a full squad available, though, and he could find himself out of the side now that Eduardo Camavinga is back to fitness.
A recent report claimed that a decision has been made over the 38-year-old's Real Madrid future, with the capital giants not planning to offer him another contract this summer.
As a result, he is set to be available on a free transfer, and according to AS, Al-Hilal remain determined to bring him to Saudi Arabia.
However, it is unclear at this stage whether the club are prepared to offer him a similar deal to the one that was placed on the table in 2023.
Al-Hilal have proved themselves to be the dominant force in the Saudi Pro League this season, picking up 53 points from their 19 league matches, which has left them top of the table, seven points ahead of second-placed Al-Nassr.
The Riyadh-based outfit, who are managed by Jorge Jesus, already have standout names in their squad in the shape of Kalidou Koulibaly, Ruben Neves, Aleksandar Mitrovic, Neymar and Sergej Milinkovic-Savic.
Modric is set to turn out for Croatia at Euro 2024, and it is understood that he has no plans to retire, believing that he is capable of playing into his 40s despite the demands of his position on the field.
The midfielder arrived at Real Madrid from Tottenham Hotspur in 2012, and he has represented his current side on 510 occasions, scoring 38 goals and registering 82 assists in the process.
Modric has won 23 trophies during a successful period at Bernabeu, including three La Liga titles, two Copa del Rey crowns and five Champions Leagues.
Real Madrid will take on Barcelona in the final of the Spanish Super Cup on Sunday evening, while they are also targeting success in La Liga, the Champions League and the Copa del Rey during the 2023-24 campaign.