And the Bernabeu club have asked Mourinho's people to inform them of any job offers he receives.
Yet a source close to Mourinho insisted there is nothing to report.
The source said: "Jose would like to talk to the FA about the England job but no one has called him. Contact has been made indirectly by a couple of individuals who know Jose and who wanted to get a feel for his view on the job.
"But Jose will only talk to the people who'll make the appointment and they haven't spoken with him."
A close pal of Mourinho said: "There has been absolutely no official approach from the FA yet.
"There has been a preliminary approach but no official approach. Jose's waiting to see if that happens."