Spurs are in talks with the Bernabeu outfit about a potential season-long move for the 22-year-old.
However, Sky Sports News reports that the Gunners are also interested in a temporary deal for the Spain international.
Ceballos is understood to prefer a loan move over a permanent transfer as he is convinced that he will be able to break into Real Madrid’s first team in the future.
However, he is currently not in Zinedine Zidane’s plans and is eager to earn regular minutes next season leading up to Euro 2020.
The report adds that the Gunners are close to completing a deal for Saint-Etienne’s teenage centre-back William Saliba.
The 18-year-old will spend 2019/20 at the French club on loan before joining up with Arsenal’s first-team squad next summer.
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