Nuri Sahin could leave Anfield this month as Liverpool look to offload the player and free up the wage bill.
The Turkish international is at the club on a season-long loan deal, but has failed to impress, making just seven appearances in the league and scoring one goal.
While Liverpool are hopeful Real Madrid may take him back early, they could be helped out by Inter Milan or Borussia Dortmund who are both interested in bringing the player in during the current transfer window.
Dortmund's director of sport Michael Zorc said the Bundesliga club, with whom Sahin played before joining Real, were monitoring the situation.
"Of course we are following Nuri's career - he's one of our lads," Zorc told the Bild newspaper.
"We said to him back then (when he left), if Nuri says that he wants nothing other than to play in Dortmund, then we will deal with the issue.
"But it has got to be manageable, and nothing has changed in that regard."
Inter are also reportedly keen to strike a deal with Real over a possible loan for the rest of the season, although that could be dependent on Wesley Sneijder exiting the club.