The Saudi Arabian side are interested in the Angolan international, who finds himself surplus to requirements at Elland Road.
Costa trained at Thorp Arch today and has been part of pre-season sessions under Jesse Marsch’s watch but did not travel on the tour of Australia and has not featured in the friendly games.
Both he and fellow winger Ian Poveda are expected to make departures before the transfer window closes on September 1.
A summer 2019 loan-to-buy move from Wolves saw Costa play a full part in Marcelo Bielsa and the Whites’ successful promotion bid, playing in 43 of 46 Championship games, scoring four goals and adding six assists.
His £16m move was made permanent in July 2020 but the arrival of Raphinha pushed Costa back down the pecking order and he was handed just 13 starts in the club’s first Premier League campaign.
Last summer Leeds sent the 28-year-old on loan to Valencia for the season but again he made only 13 starting line-ups in LaLiga and struggled to break into the team at all towards the end of the spell.
A move to AI-Ittihad would reunite him with Nuno, who signed the winger for Wolves from Monaco in January 2017 in a £13m deal.
Costa helped the Portuguese lead Wolves to promotion from the Championship in the 2017/18 season and yet, in a foreshadowing of his time at Leeds, he found himself on the bench for the majority of the second half of the club’s first Premier League campaign before moving to Elland Road on loan.
Nuno was named AI-Ittihad boss last month, eight months after his sacking by Spurs. The Jeddah club, who finished second in last season’s Saudi Professional League, handed their new head coach a contract until 2024.