The scuffle between Chelsea and Manchester City players at the end of last weekend's encounter could see the blues docked points, The Sunday Mirror reports.
Sergio Aguero and Fernandinho were sent off after a clash between the players, staff and substitutes in retaliation to the Argentine attacker's tackle on David Luiz at the end of Chelsea's 3-1 win at the Etihad Stadium.
Both teams were charged by the Football Association in the wake of the game and while it was City who saw two players dismissed, Chelsea could come away worse off from the controversy.
The Blues have already been fined four times for violating FA rules on player conduct in the past 19 months.
Notably, Chelsea were in hot water with the FA after a bust-up with Tottenham players at the end of last season, a game in which nine players were booked.
The Blues were fined heavily after that incident and warned that their repeat offences could lead to a point deduction.
If the FA were to pursue such a punishment, it would be the first time a top-flight English club has had points removed in 26 years, when Manchester United and Arsenal were punished for a battle between players.