Al-Hilal have submitted a £6 million ($8m) offer for Everton midfielder Bernard, Goal can confirm.
Bernard joined Everton as a free agent after leaving Shakhtar Donetsk in the summer of 2018, and has since racked up 68 appearances for the club in all competitions, scoring six goals.
The 28-year-old was a regular in the starting line-up over the past two seasons, but has fallen down the pecking order at the start of the 2020-21 campaign.
Summer signings James Rodriguez, Allan and Abdoulaye Doucoure have been granted prominent roles in Carlo Ancelotti's side ahead of Bernard, who still has two years left to run on his current contract at Goodison Park.
Goal has learned that Al-Hilal are hoping to lure the Brazilian to the Saudi Pro League before their transfer window closes on October 25.
The Middle Eastern club have already lodged a formal bid for Bernard, having identified the playmaker as a priority target, but he has made it clear that he would prefer to stay in the Premier League.
Sporting CP forward Luciano Vietto and Santos winger Yeferson Soteldo are also on Al-Hilal's shortlist as Razvan Lucescu seeks to bolster his attacking ranks.
The Saudi Arabian outfit have reportedly seen a €7m (£6m/$8m) bid for Soteldo accepted, but the club have yet to confirm whether the transfer is going ahead.
As it stands, Bernard will remain at Everton and fight for a place in Ancelotti's team until at least January, when he will have the opportunity to rethink his future depending on his position in the squad.
The Toffees have soared to the top of the Premier League table without the Brazil international, winning four and drawing one of their opening five matches.
Ancelotti's men earned a credible 2-2 draw against reigning champions and local rivals Liverpool in their last outing at Goodison Park, with goals from Michael Keane and Dominic Calvert-Lewin cancelling out efforts from Sadio Mane and Mohamed Salah for the visitors.
Everton are due back in action on Sunday when they take in a trip to St Mary's to face Southampton, which comes seven days before they negotiate another away fixture against Newcastle at the start of November.