The Spaniard spent the recent campaign on loan with Real Madrid. He was signed as an emergency cover after Thibaut Courtois’ serious knee injury.
Arrizabalaga made a handful of starts under manager Carlo Ancelotti before he was displaced by Andriy Lunin, who was fantastic between the sticks.
The former Athletic man is set to return to the Blues for pre-season training, but Marca claim that he currently has an offer from Al-Ittihad in Saudi.
Arrizabalaga does not want to make a rushed decision on his career and he is prepared to assess potential offers in the coming weeks before his verdict.
Lunin is currently eyeing a fresh challenge away from Madrid. He is reluctant to play second fiddle to Courtois in the next campaign.
His potential exit could see Madrid return for Arrizabalaga. The Spaniard is said to be open to reuniting with the reigning European champions.