Frozen out by Zinedine Zidane, the 24-year-old moved to the Emirates in July 2019 on a season-long loan.
He returned to the Gunners on loan again in September with Zidane admitting he would not get the playing time he wanted at Real.
But in an interview with Spanish media, Ceballos has now made it clear he still sees his long-term future in Madrid.
He said: “My goal one day is to return to Real Madrid and be important in the best club in the world.
“I believe that one day I will come back and be able to return the affection that the fans showed me. For various reasons, I didn't leave the club in the best manner.”
Ceballos is still in close contact with his Real team-mates and feels he still has time to prove himself at the Bernabeu.
Real signed the Spain midfielder from Real Betis in 2014 for around £16m, and Ceballos also admitted he wants to return to his old club at some point in his career.
Ceballos, who has made 23 appearances for Arsenal this season, recording one assist, told El Larguero : “One day I will return to Betis.”
Arsenal have explored the possibility of signing Ceballos on a permanent deal but he remains under contract with Real Madrid until 2023.