Van Gaal said Falcao must play in the second team before he would be considered to start a game and "was not interested" if the 28-year-old was unhappy with his current role.
"He is not fit enough to start a game yet. He needs to play 45, 60 or even 90 minutes in the second team but I haven't been able to do that because I needed him on the bench when James Wilson missed the Hull game and Wayne Rooney was injured for the Stoke game," Van Gaal told a press conference.
"I selected him (on the bench) despite the fact that, at the moment, he can only play 20 minutes at that level because the physical intensity in the Premier League is the highest in the world.
"I am not interested (if he is unhappy being on the bench). He has to follow my philosophy."
Taron however disputed the Dutchman's claims.
"100 percent ready to give everything," she posted on Instagram alongside a photograph of Falcao smiling during a training session.
It is not the first time a player's partner has taken to social media to defend her man.
In May, Samir Nasri's girlfriend, Anara Atanes, launched a scathing Twitter attack against France coach Didier Deschamps after he opted not to select the Manchester City winger for the 2014 World Cup.
In 2013 Kissa Abdullah, girlfriend of Stoke City forward Kenwyne Jones, condemned his team mates "disgusting" joke after they put a pig's head in his locker.
(Reporting By Tom Hayward)
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