Perez will meet the media at the club's Bernabeu stadium at 20:00 (CAT).
Mourinho's contract runs until 2016 but it is widely expected that he will leave Madrid to return for a second spell at Chelsea.
A 2-1 defeat to Atletico Madrid in Friday night's Copa del Rey final meant Real will end the season without a major trophy and has accelerated claims that Mourinho could make a return to Chelsea, a team which he previously managed between 2004 and 2007.
The favourite to replace Mourinho at Real is Carlo Ancelotti, who told his club Paris Saint Germain on Sunday that he wanted to leave.
PSG have warned Real that the Italian still has one year left at the newly-crowned French champions.