Silva has a £6 million release clause in his deal and just one year left on his contract with the Cottagers.
There has been a lot of noise surrounding Silva. West Ham United wanted him to replace David Moyes and other Premier League clubs have looked his way.
Silva caught the eye last season, leading Fulham to a tenth-place finish in the Premier League.
Many people predicted immediate relegation in their first season back in the top flight, but they survived easily.
However, they could lose Silva with Al-Ahli making an enticing offer. They have reportedly offered the 46-year-old a two-year deal worth around £40 million.
Silva’s agents are in London to discuss a deal with Saudi officials.
Al-Ahli want to conclude a deal soon as they have already started pre-season training in Austria.
The Saudi club is currently working to sign Riyad Mahrez from Manchester City after the Algerian accepted their offer.
They are also pushing to sign Newcastle United winger Allan Saint-Maximin. Roberto Firmino and Edouard Mendy have already joined the club.
Fulham face some tough decisions ahead of next season, with their manager and striker Aleksandar Mitrovic being targeted by Saudi clubs.
Al-Hilal are chasing Mitrovic and have already submitted a first offer for the Serbian centre-forward, which Fulham rejected. They are asking for £52 million.
Mitrovic has his heart set on the move to the Middle East. He begrudgingly returned to pre-season training but has told them he wants to leave.