Hakimi is in the second part of a two-season loan deal from the 13-time European champions.
The 20-year-old broke into the Real Madrid first team in the 2017/2018 season, making nine La Liga appearances but was sent out on loan the following season to continue his development.
Hakimi has impressed as one of the best young full-backs in Germany, making 21 appearances in the Bundesliga last season as Dortmund came agonizingly close to winning the league title.
Hakimi has continued from where he left off last season in the current campaign and scored twice in the UEFA Champions League in midweek when Dortmund run away 2-0 winners away to Slavia Prague.
Dortmund have made clear their intentions of keeping Hakimi permanently, but while he is flattered by their confidence shown in him, his main aim is to succeed in the Spanish capital.
"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."
