Mourinho has seen his managerial career slip over the past four years during his time in the Premier League.
Despite jumping at the opportunity to take the job, the former FC Porto manager never got going at the Santiago Bernabeu and was replaced by youth coach Solari in October 2018.
"There is the option of bringing in Mourinho now, but to me there is no point".
Jose Mourinho, who previously managed Madrid before returning to England with Chelsea in 2013, has also been mentioned in relation to the position. After dropping 12 points behind Barcelona in the league table, the lone competition remaining for Madrid to hang its hat on was the Champions League.
"The first option for the president has always, always been Mourinho", Calderon said. Other names being mentioned include Juergen Klopp, Mauricio Pochettino, Joachim Loew and Antonio Conte, who was highly touted to replace Julen Lopetegui when the former Spain coach was sacked a few months into his job with Madrid this season. Because of this, the deposed European champions are said to be ramping up their efforts to find a new manager to take over from Santiago Solari at the end of the season.
The former Argentina and Madrid player has led the team to 21 wins, eight losses and two draws in 31 matches in all competitions.
They also claim Perez wants Solari to be dismissed before Sunday's La Liga meeting with Valladolid.