Netherlands star Van Persie has not featured for United since leaving the Liberty Stadium in a protective boot after the 2-1 defeat at Swansea City in late February.
Van Gaal has already ruled the striker out of Saturday's contest against Aston Villa and confirmed he does not foresee the former Arsenal man being fit by the time champions City visit Old Trafford on April 12.
"I don't think so," Van Gaal replied when asked if Van Persie would play against Manuel Pellegrini's men.
"The process has to give me signals he is ready for that but I know that from my experience it is not like that."
United won four straight Premier League matches before the international break - including the notable scalps of Tottenham and rivals Liverpool.
That has left United just two points adrift of second-placed City and Van Gaal believes catching their local rivals is a realistic target.
"Of course [it is possible]. I cannot deny that because we have Manchester City at home," he added.
"We have the strongest record at home so it's possible, but Manchester City is a top team so it shall not be easy."
