After the game, the FA requested Chelsea's CCTV footage of the incident and also said that referee Alan Wiley would have been in his dressing room, a long way from the scuffle.
There are varying reports about the incident, being dubbed the "Battle at the Bridge".
Manchester United players accused Chelsea staff of provoking the brawl.
Striker Carlos Tevez was quoted in the Guardian claiming team-mate Evra was subject to a "grave insult".
The Argentine added: "I think that the security cameras will show the provocation we received. I have never seen anything like this in my career... if the FA opens an investigation, we will co-operate and happily give our version of what happened."
Chelsea's dossier reportedly alleges more incidents involving United players than those which have already been highlighted.
When the clubs were contacted by BBC Sport on Thursday, neither would comment on what has been put in the dossiers.
The two are also locked in tense battles on the pitch as they contest the Premier League and Champions League crowns in a thrilling end to the season.
The duo are level on points at the top of the Premier League going into the last match of the campaign on Sunday while they will play in the Champions League final in Moscow on 21 May.