Real's 1-0 Champions League defeat in Lyon has increased the pressure on Manuel Pellegrini, and sources in Spain claim the Spanish club received a positive response when Mourinho's representatives were approached.
The Special One: Jose Mourinho could leave Inter this summer
Mourinho has three years to run on his Inter Milan contract but this can be terminated for £6m during the summer.
Roberto Mancini's agreement with City stipulates a get-out clause after six months and after a bright start as Mark Hughes' successor the Italian is struggling to maintain that early momentum.
Mourinho has made no secret that he would like to return to English football but the prospect of winning a title in a fourth country may sway the Portuguese towards Madrid.
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