The Manchester United forward's three goals helped his team to a 4-2 victory at West Ham on Saturday which took them seven points clear at the top of the Barclays Premier League. But, after completing his treble, the striker uttered an audible expletive into a television camera as he celebrated.
The Football Association's director Sir Trevor Brooking told BBC Radio 5 Live's Sportsweek programme: "Tomorrow (Monday) there will be a decision. It was a surprise, after scoring a hat-trick, to react that way. It is something we will have to look at."
Rooney has already apologised for swearing.
His outburst, beamed around the world by Sky Sports, prompted an on-air apology from the broadcasters.
In a statement released by United, Rooney said: "I want to apologise for any offence that may have been caused by my goal celebration, especially any parents or children that were watching. Emotions were running high, and on reflection my heat-of-the-moment reaction was inappropriate. It was not aimed at anyone in particular."
There is recent precedent of disciplinary action against a swearing sportsman, England cricketer Graeme Swann having been fined 10% of his match fee in the World Cup defeat by Bangladesh in Chittagong last month - although on that occasion, the player did not direct his words deliberately towards a camera or stump mic.
In football, the disciplinary procedure in such circumstances is less obviously established.
But FA rules 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.
Source: PA
Source: PA