Van Gaal said that the Colombian suffered a knock in training on Friday morning and admitted that 18-year-old striker James Wilson could replace him in the squad.
Falcao missed the World Cup in the summer after sustaining cruciate knee ligament damage back in January, but the Dutchman was keen to stress that his latest knock is not related to that injury.
"He got a kick in the morning [on Friday] so we have to wait and see if he's fit enough," he told reporters. "But it's not a knee problem.
"He had a knee problem but not anymore. We have to build Falcao up, that I have also said in the first press conference when he came to our club.
"It is difficult because we are playing [games] already, that's difficult but we have played him because I like the way he was playing so we play with two strikers. Now I have to choose between two strikers, even three because [James] Wilson can also play, the younger player."
Wilson scored twice on his United debut back in May - a 3-1 win at home to Hull City. However, he has only played 17 minutes of Premier League football this season.
Falcao, who is on a season-loan loan from AS Monaco, has netted once for the Red Devils thus far.