Morata is back at Real after the club re-signed him from Juventus last week for £23m but the club are expected to sell him on again at a profit.
El Confidencial say that the European champions are looking to get in the region of £50m for the Spain international.
They said he was keen to play under Mourinho again after the Portuguese boss handed him his debut at Real in 2010.
Meanwhile, El Confidencial claim Varane is ready to press for a move away from the Santiago Bernabeu as he no longer wants to be third choice centre-back.
Sergio Ramos and Pepe are established as Zinedine Zidane’s first-choice pairing and the report says that a change of scenery would be best for all parties.
Mourinho is a keen admirer of the France international, having signed him for Real from Lens in 2011, and the Manchester Evening News have reported that United would pursue a deal if he was available.
Varane is valued in the region of £40m.