Los Blancos followed up their loss to Sevilla before the international break with a four-goal defeat at home to Barcelona in the Clasico at the weekend.
That leaves Madrid six points behind Barca, who lead the table, while Atletico Madrid leapfrogged them into second place with their win over Real Betis on Sunday.
READ MORE | Ronaldo's Madrid love affair over?
Benitez replaced Carlo Ancelotti in the summer and has never truly been accepted into the role.
The former Liverpool boss has had to deal with unrest from fans and from players - only last week he was forced to deny that three senior players had asked him to alter his defensive style in a meeting.
Madrid announced the media conference via a statement on Monday.
It read: "The Real Madrid C. F. president, Florentino Perez, will hold a media conference at 6:30pm GMT this evening in the Santiago Bernabeu following the board meeting."
Despite the pressure surrounding Benitez, who's been in the job for less than six months, it was not the Spanish coach who Madrid's fans turned on during the Clasico.
There were boos for their star player Cristiano Ronaldo, while there were regular chants for Perez to resign as president.