The 22 year-old Turkey midfielder is under contract until 2013 with Borussia, who host Freiburg on Sunday in the Bundesliga, but Dortmund says they expect to lose him once the season ends on 14 May.
He has a clause in his contract that he can leave if a club offers at least six million EUROS for him and is reported to have already received an offer from Real Madrid, where his friend Mesut Ozil plays.
"If Nuri receives an offer from Real Madrid or Barcelona, he has every right to talk about it with us," Dortmund CEO Hans-Joachim Watzke told German daily Bild.
"We would like to have extended his contract already, but unfortunately we have not yet succeeded in making that happen.”
Dortmund have already been linked to Nuremberg's playmaker Ilkay Guendogan as a replacement for Sahin, should the Turkey star leave.