Marca comments that the capital club will confirm the deal on their official website tomorrow when both Dortmund and Sahin will hold a press conference in Germany simultaneously confirming the switch.
The German-born Turkish midfielder will sign a five-year deal with Madrid paying Dortmund around €10 million for his services.
Madrid chief Jose Angel Sanchez is expected to fly to Germany in the morning in order to allow the 22-year-old to sign the agreement.
Reports in the German media too suggest that Sahin will make the switch to the Spanish giants this summer and that the decision will be made public tomorrow.
It is being also reported that the press conference will be held at 12:30 CET on Monday and that the player’s agent will be present alongside him.Sahin is currently injured and is expected to continue treatment for a knee injury with the Spanish club once he joins them.
Meanwhile, speculation is that the whites will also move for Bayern Munich's Hamit Altintop, who has been tipped as the next player to join Jose Mourinho's outfit next season.