BILD says Real scouts have been studying Glasner for over two seasons and have added him to their shortlist of future coaching targets.
The success of Eintracht Frankfurt has confirmed Glasner's qualities to Real, which have placed him on a top five list of coaching candidates.
For the moment, Carlo Ancelotti is safe, but Real always have contingency plans in place.
It's also emerged Tottenham made recent enquiries for Glasner.
Eintracht sports director Markus Krösche, however, does not want to lose the Austrian.
When asked if someone had contacted him, the 41-year-old replied at a press conference yesterday: "No, and he can save the nine cents for the call."
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