At the start of last season, Arrizabalaga was surprisingly allowed to move to Los Blancos on a straight season-long loan deal to replace the injured Thibaut Courtois.
Arrizabalaga would make a total of 19 starts and one substitute outing in all competitions, losing his spot in the starting lineup during the second half of the campaign.
With Courtois having since returned to full fitness to regain the number-one position ahead of Andriy Lunin, Real felt no need to make an approach to sign Arrizabalaga on a permanent basis.
As a result, the 29-year-old has been forced to consider his options with there being no prospect of extending his contract at Stamford Bridge past 2025.
Although there has been speculation regarding a potential switch to the Saudi Pro League, there is no more currently in the offing.
"We love him"
With Lunin as deputy to Courtois, there is no prospect of Arrizabalaga returning to the Bernabeu, but the situation may change in due course.
Lunin has just a year remaining on his contract, Real naturally wanting the Ukraine international to make a decision either way in order to avoid the risk of losing the stopper on a free transfer.
The issue with his goalkeepers and Arrizabalaga came up when the English media interviewed Ancelotti, the legendary Italian hinting that re-signing the Spain international remains a possibility.
As quoted by TEAMtalk, Ancelotti said: "Kepa did really well last season. We were really happy to have him here, but I don't know what's going to happen this season.
"We love him. We love him."
Would transfer suit all parties?
Even with the prospect of Courtois playing the majority of games in 2024-25, Arrizabalaga has previously suggested that he wants to continue to represent Real.
Chelsea have recently signed Filip Jorgensen to compete with Robert Sanchez, with Djordje Petrovic in line to be sold or loaned out before the end of the month.
Even if the latter occurs, Arrizabalaga will not be pushed up the pecking order, the powers-that-be at Chelsea wanting a sale in order to get the former Athletic Bilbao man off their wage bill.