The Dutchman has already been ruled out of this Saturday's league game at home to Aston Villa and asked if he would be fit to face City on April 12, Van Gaal said: "I don't think so.
"The process has to give me signals he is ready for that but I know that from my experience it is not like that."
Van Gaal earlier told MUTV that Van Persie was recovering along with left back Luke Shaw, who has been out with a hamstring injury.
"Robin is coming back on the (training) pitch and Luke Shaw has already had a week on there but match rhythm is very important," said Van Gaal.
"You cannot compare a player who has been out for four or five weeks to those that have sufficient match rhythm."
Van Gaal explained later in his news conference: "We have a process for injured players in the medical department, they then go to a football coach for tests and then to me.
"Robin still isn't with the football coach. He's still not in my group. Luke Shaw is in my group, that's different, but Van Persie isn't available."
United are fourth in the standings with 59 points from 30 games, a point behind Arsenal and two adrift of City. Chelsea, who United visit on April 18, are top with 67 points.
(Writing by Ken Ferris; Editing by Peter Rutherford)
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