Rooney uttered an audible expletive following the completion of his hat-trick at Upton Park, which helped United come from 2-0 down to win 4-2.
The lunchtime Barclays Premier League game was beamed around the world by Sky Sports and Rooney's outburst prompted an on-air apology from the broadcasters.
The FA confirmed they would examine footage of the incident but it was unclear what action, if any, they would take.
"We will look at it," a spokesman said.
"We obviously don't condone foul and abusive language."
It is understood taking action over a player swearing at a camera during a game may be unprecedented.
But there does appear to be provision for sanction in the FA's own rules about behaviour, which state: "A participant shall at all times act in the best interests of the game and shall not act in any manner which is improper or brings the game into disrepute or use any one, or a combination of, violent conduct, serious foul play, threatening, abusive, indecent or insulting words or behaviour."
Rooney upset England fans during last summer's World Cup when he turned to a television camera and verbally attacked them at the end of the dismal goalless draw with Algeria.