They are out of Europe, lost to Barcelona in the semi-final of the Copa del Rey and are third in La Liga - five points behind second-placed Atletico Madrid and a further seven off leaders Barca.
Mourinho is available having been sacked by Manchester United in December 2018 after a dismal set of results and style of play left the board with no other choice but to replace him with Ole Gunnar Solskjaer.
Solari walked into Wednesday's Champions League game against Ajax with a knife over his head as rumours of a successor for the job have already been doing the rounds.
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"The first option for the president has always, always been Mourinho", Calderon said.
Merengues supporters sang the name of their former coach, who led the club from 2010-13, outside the Bernabeu after the 5-3 aggregate defeat. They are talking of the possibility of Zidane or Mourinho - they are completely different coaches with completely different ideas of football.
With Mourinho's agent Jorge Mendes believed to be in talks to secure his client's return to Real Madrid, the discussions now revolve around the length of his contract and whether he will continue in the role beyond next summer.
"At this moment of the season anything you do is going to be wrong, I suppose that they will wait until the end of the season but this is very long time, three months, to suffer all the critics and the anger of the fans".