Sahin, who is still on Real Madrid's books since joining them in the summer of 2011, and is on a season-long loan with the Reds, has struggled to settle since leaving Germany.
Sport Bild reports that tensions with Liverpool skipper Steven Gerrard have hampered his performances and appearances at Anfield, while claiming Sahin has been disappointed with the scale of his role at the club.
Borussia Dortmund appear to want him back, with CEO Hans-Joachim Watzke hailing his ability in an interview with the paper.
"Sahin only feels good when a team is built around him," Watzke said.
"He is a fantastic guy, and with a great temperament. And a super footballer."