City boss Pep Guardiola is in the market for two new centre-halves - with Varane on his radar.
However in Madrid, there's a confidence of not losing the France international. Real chiefs see Varane as the man to eventually succeed captain Sergio Ramos.
The Manchester Evening News says if an opportunity were to come up, City would jump at it.
However, Real intend to oppose any interest from the Sky Blues for Varane.