The Gunners have been heavily linked with the Spaniard, even before he moved to the Bernabeu in the summer, but the Spanish publication say neither the player nor Real would sanction a switch to the Emirates.
Ceballos is reportedly keen to stay in Spain, and is believed to want to return Real Betis, who he left to make the move to Madrid in July.
Real meanwhile do not want the 21 year old to join a European rival, and would like the player to join a team like Bundesliga side Eintracht Frankfurt, who they have good relations with.
Regardless of his destination though, the Spanish international is determined to leave in the summer after being used sparingly by manager Zinedine Zidane.
He has managed just 19 appearances in all competitions this season, with his last match coming as a substitute in the 1-0 defeat to Espanyol back in February.