The unsavoury fracas involved six of United's players, Chelsea groundstaff and several match day stewards. The FA have already confirmed they want to see CCTV footage of the incident.
United boss Sir Alex Ferguson said: "We are filing a report which will be sent to the FA.
"We are very happy with that, we are delighted with that.
"We hope the FA investigate it."
It is also believed that Chelsea and Manchester United chief executives Peter Kenyon and David Gill have discussed the incident, which was sparked when the players were asked by groundstaff during their warm-down session to run in the same direction as lawnmowers being used to trim the playing surface.