The 24-year-old has endured a mixed two years in North London, contributing five goals from 52 appearances in the Premier League.
With the Frenchman possessing a long-term contract, Spurs remain in a strong position regarding the playmaker's future.
However, according to Football Insider, Real are contemplating whether to test Spurs' resolve during the summer window.
Although the report claims that the English side are aware of Real's interest, no decision has been made over whether Ndombele will be allowed to depart his current club in the near future.
At a time when Ndombele has spent time out of the side under caretaker boss Ryan Mason, Spurs are expected to wait until they appoint a new full-time manager.