Gunners boss Arsene Wenger is scouring the transfer market as doubts surround the future of Mesut Ozil and Alexis Sanchez and it would appear that Ceballos is a target.
The 21-year-old only arrived at the Bernabeu in the summer when signing from Real Betis, but he has failed to establish himself in the Los Blancos side despite them struggling to hit form this season.
That has kicked off suggestions in Spain that Real boss Zinedine Zidane did not want to sign Ceballos in the summer, and the transfer was the wish of Florentino Perez.
Either way Ceballos wants regular first-team football, after making just two league starts this season, and is willing to move away from the Bernabeu in the new year to get it.
There will be no shortage of interest either and Arsenal will face strong competition from Tottenham and Italian giants AC Milan should they pursue a deal.