The board is discussing the future of the manager after the club's defeat at Norwich.
Sky Sports News understands that Saturday night's meeting is the latest in a series of disagreements between the board and owner of the club.
The Spaniard has failed to win over the Goodison Park faithful despite being appointed as the boss of the club last summer.
Fans of the club displayed a banner calling for his departure after the loss to the Canaries. The same banner was unfurled at the FA Cup win.
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There are free to watch highlights from the game.
The banner was unfurled by the fans of the club against their manager.
In the past 13 league games, the Toffees have lost nine of them, including a 4-1 home defeat by the Reds and a 5-2 home defeat against the Hornets.
After the defeat, he was asked about his future. He said he has enough experience to be a professional.
I came here to fix things that have been happening for the last five years. I have to analyse the mistakes we are making and make sure they are not repeated in the future. The rest is not in my hands.
Benitez's record is at Everton.
P22 W7 D5 L10 F31 A39
Each of their last 9 games has seen them concede the first goal, as they have conceded the first goal in 16 of 22 games this season.
This is the third time in the last four years that they have had fewer points at this stage of the campaign than they have this season.
The next games forEverton.
January 22: Villa.
The FA Cup will be played on February 5.
February 8 is the date of the premier league.
February 12th, 2015: Yorkshire (H) - premier league
February 19th, 2015:Southampton
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