The 21-year-old burst onto the scene earlier this season, scoring twice on his first start for Los Blancos in a 2-1 victory over Alaves in September.
Ceballos has featured 13 times in all competitions for Real, but eight of those appearances have been from the bench.
According to Diario Gol, the Spain Under-21 star regrets choosing Madrid over Barcelona when he left Real Betis in the summer after receiving no guarantees over more playing time.
The report also suggests that Ceballos is aware of Zidane's time at the club "coming to an end" but despite this, the midfielder will still seek a departure from the Bernabeu.
A number of clubs including Liverpool, Roma, Inter Milan, Tottenham Hotspur and Arsenal are all believed to be interested in Ceballos's signature.