The 30-year-old was a peripheral figure at Stamford Bridge in the 2022/23 season where he featured in just 18 Premier League games.
He started just six times in the top-flight as the Blues finished 12th in the table.
Having been deemed as surplus to requirements by former boss Graham Potter, the Morocco international was in talks to join Paris Saint-Germain in January.
But that transfer fell through despite Ziyech passing a medical in the French capital after Chelsea sent the correct paperwork three minutes after the window closed.
And after missing out on calling Lionel Messi a teammate, Ziyech, who still has two years left on his deal in west London, could now play alongside Ronaldo.
READ MORE ON CHELSEA
Havertz compared to Ozil as 'concerns' revealed about Arsenal target after rejected bid
Mudryk inspires Ukraine to comeback win with two stunning assists to match Chelsea haul
According to Foot Mercato, Al Nassr are ready to offer the ex-Ajax star a huge contract offer.
It has been said that Ziyech is seriously considering their proposal as he knows he isn't in Chelsea's plans going forward.
Club president Musalli Al-Muammar is also alleged to be set to travel to London to tempt the player into joining.
Ziyech may not be the only Chelsea star to swap Stamford Bridge for the Saudi Pro League.
Most read in Football
Man United transfer news LIVE: Mount bid readied, Watkins eyed, Pogba calls out fans
Manager that Ronaldo 'got sacked' at Al Nassr backed to win Champions League with Napoli
Ten Hag double blow as defender heads to Bayern and 'next Haaland' given mammoth price tag
Man United target beats Kylian Mbappe to Ligue 1 player of the season gong
French World Cup winner N'Golo Kante has been heavily linked with a move to champions Al Ittihad when his contract expires at the end of the month.
Meanwhile talkSPORT understands that Romelu Lukaku is attracting interest from Saudi sides as Chelsea desperately look to get the Belgian off their wage bill.