The Netherlands star has been linked with a move to Old Trafford despite his recovery from a serious knee injury, and the Red Devils boss admits he is keeping a watching brief
The Dutchman was in impressive form for Roma last season until a serious knee injury curtailed his campaign in March - ending his chances of being included in Van Gaal's Netherlands squad for the World Cup.
The midfielder remains a target for United, with the club prepared to wait for the chance to sign the midfielder, but Van Gaal insists he must wait to see how he recovers from his injury.
"I never say anything about individual players. It is my vision that we talk about a team and not individual players," he told reporters.
"Strootman I can judge, but he is injured for more than six months. We have to wait and see how he comes back.
"It is not easy to say how he comes back from injury, but we will wait and see."
Roma boss Rudi Garcia, meanwhile, has insisted that the 24-year-old will not be leaving the club this summer.
"I have never discussed his departure and neither has he," he told the press. "Strootman is a Roma player and he'll stay with us this season."
Garcia also revealed that Strootman will not be in Denver on Saturday when Roma face Manchester United in a pre-season friendly.
"Kevin is following a personalised rehabilitation programme and I don't want him travelling unnecessarily, so it's best he remains in Boston to work with the physiotherapists," the Frenchman added.
"He should resume running soon, so he's in good shape."