With the Toffees also vying for a ticket to European football, Koeman has stated he doesn't think United can cope without injured talisman Zlatan Ibrahimovic, who was recently ruled out for the rest of the season.
"I cannot see Manchester United finishing in the top four," the Dutchman was quoted as saying by the Express.
"Zlatan's injury looks bad and when I look at the amount of matches they are having to play this season, I can see them missing the top four.
"I have not been impressed by the way they play," added Koeman.
Jose Mourinho's men, whose main focus is the Europa League, have a tough league run-in which will see them travel to the Etihad, the Emirates and White Hart Lane.