Madrid president Florentino Perez will speak to the media at 7pm Irish time at the club's Bernabeu stadium, the Spanish giants have announced in a statement on their website.
Madrid have not given any details regarding the subject of the press conference but the future of Mourinho has dominated Spanish media since Real's Copa del Rey final loss to Atletico Madrid on Friday night.
Mourinho, who last summer signed a contract extension with Madrid tying him to the club until 2016, has been closely linked with a move back to former club Chelsea.
The 50-year-old Portuguese has helped Madrid claim three trophies during his three years at the Bernabeu, winning the Primera Division, Copa del Rey and Spanish Supercopa. However, they failed to defend their league title this season, surrendering it to arch rivals Barcelona, and suffered further disappointment with their cup final defeat to Atletico their first loss to their neighbours in 14 years.
During Mourinho's tenure, Madrid also suffered three successive semi-final exits in the Champions League a competition the club have been desperate to win since their ninth and last triumph in 2002.
According to reports in Spain, the press conference could also see Perez confirm details about this summer's presidential elections at the club as well as possibly talking about the coaching situation.
Carlo Ancelotti has emerged as the leading candidate to replace Mourinho should the former Inter Milan and Porto boss leave Madrid. Ancelotti, another former Chelsea manager, last night told Paris St Germain he wanted to leave the newly-crowned Ligue 1 champions. However, he still has a year on his contract at the Parc des Princes and the French club's owners look unlikely to let the Italian go without a fight.
Club president Nasser Al Khelaifi told beinsport.fr: "Yes, we had discussions, he asked to depart for Real Madrid. I said it is not possible because he has a contract for one year more, so that is our decision. It is his problem, it is not our problem. We have offered him another year more on his contract as well as the one he has.
"When you have a contract, everyone is normally obliged to honour that."
Ancelotti said at last night's Ligue 1 awards evening: "Real is a possibility but I have a year left on my contract. It is the club who will decide. We have to decide together. My decision is to leave the club. It is not easy because I have had a very good relationship with everyone.
"It is not the time to explain the reason why I wish to leave the club, and perhaps I will never explain it."