Ahead of the opening weekend of last season's Premier League, Arrizabalaga had been expected to be the Blues number one under Mauricio Pochettino.
Instead, a loan offer arrived from Real Madrid, the Spaniard taking up that opportunity in the hope of earning a permanent switch to the Bernabeu.
Although the 29-year-old would make 19 starts and one substitute outing for Los Blancos, he lost his place during the second half of the campaign.
As a result, Real are currently not pursuing his signature on a full-time basis, leaving Arrizabalaga to return to his parent club for the time being.
Saudi Arabia club monitoring situation
With a year left on Arrizabalaga's contract, it is no secret that Chelsea are open to offers for a player who cost £72m back in 2018.
According to Marca, there is an offer on the table from Al-Ittihad.
Their defence of the Saudi Pro League title ended in failure with the People's Club finishing down in fifth position, a massive 42 points adrift of champions Al-Hilal.
Al-Ittihad had hoped to appoint Stefano Pioli as their new head coach over the weekend, only for that deal to have been scrapped due to behind-the-scenes reasons.
Nevertheless, Arrizabalaga has allegedly been provided with a lucrative proposal to make the switch to the Middle East, one that he is currently assessing.
However, it is claimed that the former Athletic Bilbao man is in no rush to make a decision on his future, aware that other offers could materialise in due course.
Chelsea eager for quick sale
Although Enzo Maresca is now at the helm, there has been no suggestions that the Italian is prepared to reintegrate Arrizabalaga into the senior ranks.
Robert Sanchez will seemingly be promoted to first choice ahead of Djordje Petrovic, despite the Serbian doing little wrong during the second half of last season.
Chelsea also have the likes of Marcus Bettinelli and Gabriel Slonina on their books, the latter likely to go back out on loan for 2024-25.