Spurs had led the way for the 22-year-old and the Spanish side are listening to multiple offers.
Unai Emery wants to sign Ceballos on loan and Marca report that the Gunners are now at the front of the queue.
Real Madrid’s Dani Ceballos is a target for both Arsenal and Tottenham this summer
Arsenal have a transfer budget of only £45million this summer so Emery is having to add to his squad in any way he can.
He wants the option to make the deal permanent if Ceballos was to join and impress at the Emirates.
Ceballos only played 13 games for Real last season and is looking to develop and become a fixture in whichever side he opts to join.
He is in high demand after starring for the Spain Under-20s at their European championship victory last month.
Real are keen to secure a permanent deal for the former Real Betis man as they want to fund a move for Paul Pogba.
Ceballos helped Spain win the UEFA Under-20 European Championship last month