The subject of their fury are allegations that Stewart Downing was played by England against Scotland despite being injured and given a painkilling injection in order to play.
The FA deny that the timing of the injection was designed to get Downing through the game.
However, the Mirror's report states that the dispute could end up in court, with the Hammers in the 'very early stages' of trying to investigate the true nature of the incident.
"The load of constant performance at the highest level takes it’s toll across the whole of the Premier League.
"The demand on the player is so great for so long, so often that eventually they are going to break down at some stage.
"If you look at the load this year on players, it gets greater than ever before. Not only do they travel at international level across the world but the constant pressure of the Premier League is every getting faster and more demanding physically and mentally."