Reports in Spain had suggested that Real have already got a verbal agreement with Gundogan to move to the Bernabeu when his contract expires in 2015.
However, last week the player's agent and father told reporters that his son's future remained "completely open".
Dortmund also remain hopeful the 23-year-old can be persuaded to extend his contract with the Bundesliga side and that has got Real looking at a back-up plan.
Reports in Germany suggest that Dortmund will not start talks over an extension until Gundogan returns from a long-term back injury.
And, while there are no suggestions presently that the injury could have lasting effects, the German clubs caution has given Real even further reason to look at alternatives.
