The Football Association has given Stoke and QPR a week to respond to the probe on the Simon Royce attack.
QPR keeper Royce is understood to have been rushed by home fans on the pitch at the end of the 2-1 win at Stoke.
An FA spokesman said: "We are in communication with the police and the clubs as we seek to gain a better understanding of what unfolded.
"Stoke and Queens Park Rangers have a week to formally respond."
Staffordshire Police said the fight started shortly after the full-time whistle at the Boothen End in front of the QPR goalmouth, after QPR had won the match.
Players from both sides ran to assist Royce, but they then appeared to wrestle between themselves. Stewards also became involved and the fracas lasted three minutes.
Four of the men were arrested for pitch encroachment and two for public order offences. They were released on bail.
The FA have wide powers at their disposal including fining the club, forcing them to play a future game behind closed doors and even docking points.
A number of factors are taken into consideration before any punishment is handed out, such as a previous history of crowd trouble and the security measures in place on the day.
Stoke chief executive Tony Scholes told the Stoke Evening Sentinel: "We are taking seriously what happened after Saturday's game, but at the same time we don't want people to get carried away,
"We have already had around 200,000 people go through our turnstiles this season and this is the first sign of any trouble.
"This was an isolated incident involving two individuals. The rest of the crowd behaved impeccably.
"As for our stewarding, our operation at the ground is regarded by the rest of the Football League as being a model of good practice."