The 21-year-old is set to leave Dortmund at season's end but not necessarily for a return to the Santiago Bernabeu in Madrid.
"Real Madrid are the club I call home," Achraf, who has scored 10 goals during his time with Dortmund, told Telefoot. "I've really enjoyed myself there and played lots of games there.
"If Madrid want me to go back, I'll go back. And if not, I'll have to write the next chapter at another great club."
Achraf added: "[Madrid head coach Zinedine] Zidane is the man who gave me my chance and the confidence to be able to play professional football.
"I'm grateful to him for his faith in me and the way he has treated me. I'll always be grateful to him."
Reflecting on his decision to move to Dortmund, Achraf said: "When I stop and think, I realise that it was the best decision I could have made, because I'm playing and developing as a footballer, which is what I need to be doing."
Dortmund won the opening leg 2-1 thanks to Erling Haaland's second-half brace and Achraf is eyeing silverware.
"I hope we can achieve as much as possible; in the short term beat PSG, and in the longer term try to win a trophy like the Bundesliga or go as far as possible in the Champions League," said Achraf, who has scored seven goals in all competitions this season.
"Anything's possible. Hopefully we can go as far as possible and win it if we can. And if not, then come away with the feeling that we've done well and given our all."