The Portuguese manager spent three seasons with the La Liga giants, before he left in 2013 and headed back to Chelsea.
Carlo Ancelotti, who replaced Mourinho at the Santiago Bernabeu, is under intense pressure and might leave when the season ends, with Madrid set to finish without any silverware.
According to Spanish football expert, Guillem Balague, the club chiefs have drawn up a list of potential replacements, which includes Mourinho, Jurgen Klopp and Rafa Benitez.
“The idea is that Real now look for another coach – that is what normally happens when Real Madrid do not win,” he told Sky Sports’ Revista de La Liga.
“Real have spoken to Julen Lopetegui at Porto, to Jurgen Klopp, to Rafa Benitez and Jose Mourinho.
“They have already spoken to those four to see if they would be interested in coaching Real Madrid. They have spoken to Jose Mourinho – he said no to them, of course.
“Out of those four, Rafa is favoured by some but not others. Mourinho is favoured by some and not by others and Lopetegui is deemed as something for the future, but they have sounded out all of them.”
Ancelotti – who has been linked with Manchester City – might end up staying in Spain, if the club fail to find a successor.