This was made known by a respected journalist, Francesc Aguilar, who works for Mundo Deportivo.
According to Aguilar’s report, Mourinho wants Madrid to sign a new centre-half and a striker.
If the conditions are met, he will be returning to the club which he managed from 2010-2013.
During his spell with the Spanish giants, he won the La Liga and the Copa del Rey before returning to England for a second spell with Chelsea.
He was sacked few weeks ago as manager of Manchester United.