A number of clubs have been reported as being interested in the 23-year-old, who helped the Bundesliga side reach the final of last year's Champions League, where he scored in a 2-1 defeat to Bayern Munich.
Los Blancos are believed to be among the frontrunners to land the deep-lying playmaker, although Arsenal and Manchester United are also said to be monitoring the situation.
With Die Borussen stalling on a new contract offer, reports had suggested that a deal with Madrid was already in place, but Gundogan's father has rebuffed those claims.
"There is no agreement between Gundogan and Real Madrid," he told Kicker.
"We only stopped contract negotiations with Dortmund because we do not want to disturb him during his injury.
"Obviously, it is possible that he will extend his contract."
Gundogan's contract at the Westfalenstadion runs out in 2015.