The 20-year-old is a little over halfway through a two-season loan spell with Dortmund and has established himself as a first-team regular under Lucien Favre.
Achraf has predominantly been fielded at full-back but was used in a more advanced left-wing position against Slavia Prague in midweek, the Morocco international further highlighting his versatility with both goals in the 2-0 win.
He progressed through Madrid's academy and is confident in his ability to prove his worth at the Santiago Bernabeu, though his only focus right now is on continuing his development with Dortmund.
"I'm not going to lie, I'd love to be a success there, of course," he told AS. "I grew up at Madrid, it's the club I call home and I'd like to keep on growing as a player there, but if it isn't to be I'll look to be a success somewhere else.
"Right now, I'm only focusing on taking each game as it comes and performing to the best of my ability. Next summer's still a little way off and we'll just have to see what happens.
"I shouldn't start thinking about next year - I just have to concentrate on having a good campaign. That's the only way I'll have options open to me come the end of the season.
"My deal here lasts for two years. When the time comes, I'll see whether I've done enough over these two years and whether I'm ready for Real Madrid.
"Right now, I feel like I'm doing well, and that if I keep playing like this I could do a job for Madrid. But I can't say whether or not I'm ready until the end of the season. Ask me in May."
Dortmund CEO Hans-Joachim Watzke made it clear earlier this week that he will do everything possible to sign the youngster at the end of the season, but Madrid may opt against cashing in.
Asked about Watzke's comments, Achraf said: "It's always nice, being told that they'd like you to stay for good when you've only been there for a year.
"You're left thinking that you're doing well, that they're happy with you and that you are with them too. But that's a decision which I don't think is down to me; that's something the two clubs have to talk about with each other, and with my agent.
"I'm going to keep on working to help Dortmund and hopefully we can achieve big things together."