It is understood that United players took exception to being told they could not run on a muddy part of the pitch, even though Premier League rules say the playing surface must be made available to the opposition.
A heated exchange then took place, during which one United player allegedly abused Chelsea's head groundsman and a member of the Stamford Bridge groundstaff told O'Shea: "I'll stick my pitchfork up your a**e."
The FA and Premier League are beginning their enquiries into the scenes that saw defender Evra and United team-mates fighting with Chelsea groundsman Sam Bethell on the Stamford Bridge pitch as they warmed down following the London club's 2-1 win on Saturday.
United have asked for a copy of Chelsea's CCTV footage. Both clubs are likely to be fined if an FA probe proves staff or players were to blame. Bethell said: "It was handbags. I've not lost my job."