Hakimi has spent the past two years at the Westfalenstadion and has caught the eye with his displays this season down the right-hand side.
Agent Alejandro Camano has been in constant contact with Los Blancos as Hakimi's loan spell nears its end, but the youngster is simply keen to continue playing regular first-team football, wherever that may be.
"He will link up with Madrid when the championship ends," Camano told Onda Madrid. "We'll see what happens. He wants to play games, like he has this year, when he has been a starter in all the matches.
"There is no hurry. The only aspiration he has is to play games in the path of his formation. With Madrid there's a magnificent dialogue and they want to have him on their radar. And what we want is to not be too far away from Real Madrid.
"So we will reach an agreement for whatever, whether he stays or goes, but without forgetting that his aim is to play one day for Madrid, which for him is the best team in the world.
"It could be in the short term if Madrid offer him the chance to stay now or longer term if he doesn't stay, but the aim is always the same: to end up at the best team in the world."
Chelsea and Paris Saint-Germain have also been tipped to make a move for Hakimi at the end of the season.