The United and England captain was sent off for a late challenge on Stewart Downing in his club's win over West Ham last weekend and will subsequently miss Sunday's Premier League fixture against his former club.
With United yet to string back-to-backs competitive wins together under Van Gaal, the Dutchman feels the loss of his skipper is a major blow.
However, in Mata he feels he has an ideal replacement to play just behind the strikers.
"In [Rooney's] position, Juan Mata has played very well," he said.
"I will miss Wayne because he is the captain of the team but Mata can also play very well
"You shall see [who I make captain]. I have told the players but you shall see on Sunday."
Van Gaal is still having to deal with a lengthy injury crisis after Ander Herrera became the latest player to be sidelined.
Herrera will miss the Everton game with a rib injury, while Phil Jones remains out with a hamstring problem and Marouane Fellaini is not yet ready to return from his ankle problem.
Paddy McNair will continue in defence after making his first-team debut at Old Trafford last weekend.
"It's difficult to explain. You can be fit but not match fit - that's a big difference," said Van Gaal.
"For example, Herrera is fit but he cannot play because of his rib pressure. Fellaini has trained for one week but is not yet fit to play 90 minutes.
"We have eight injuries and one suspension so nine players are not available.
"We still have three central defenders injured so [McNair] shall play. He is the only player who can play in the right-sided [central] defensive position.
"I chose him last week and he played very well. It's difficult for a player like him to maintain that level - that is his biggest challenge."
