The Spanish midfielder is attracting interest from both Arsenal and Tottenham as Madrid look to ship him out on loan.
Zinedine Zidane wants Ceballos to spend a year away from the club before returning to fight for a place in the first team.
The 22-year-old is still on holiday until July 29 after his exploits at this summer’s U21 European Championships.
But according to AS, Madrid want his future to be resolved in the next few days.
Los Blancos could even make a decision before Wednesday when they play Arsenal in the US.
The Gunners have already beaten Bayern Munich and Fiorentina during their trip across the pond.
And Unai Emery may be keeping an eye on Lucas Vazquez during Wednesday’s clash after being linked with a move for the winger earlier in the window.
Starsport understands Arsenal are leading Tottenham in the race for Ceballos.
But AS also report that Madrid will allow the player to make his own decision between the two teams.
Arsenal only have a small budget at their disposal this summer, meaning a loan deal suits Emery.
The north London outfit have only signed young attacker Gabriel Martinelli so far this summer.
But Emery has promised more new arrivals before next month’s transfer deadline.
“We are working, the club is working with the possibility to sign some new players to help us,” he said last week.
“We are doing a lot of meetings with the club, with (technical director) Edu, with Raul (Sanllehi, head of football) and also with Josh and Stan Kroenke on Monday in Denver.
“We have a clear idea to sign players to help us with quality and in the positions we need.
“We are taking with the patience and with the calm because we really want to sign players who can help us with a big performance and also because we think in the team we have very good players and young players and we also need to take the best player in some positions.”