The FA said it would look at video and closed-circuit footage before deciding whether to take any disciplinary action.
United players face fines and possible bans if they are charged with bringing the game into disrepute.
Chelsea said in a statement on Sunday that it would study CCTV footage and photographs and then "consider an appropriate course of action."
United defender Gerard Pique said the fracas was sparked by "the provocation of somebody who works for Chelsea."
"Patrice wanted an explanation but these men were very aggressive," Pique was quoted as saying in The Guardian. "All we were doing was finishing our workout after the game."
Photographs in the newspapers showed a Chelsea groundsman, identified as Sam Bethell, raising a fist toward Evra while being held back by two Chelsea staff members.
In Sunday's action, John Carew headed an 86th-minute equalizer for Aston Villa to draw 2-2 with Everton in the Premier League.
Everton twice went ahead at Goodison Park, but three late goals in seven minutes gave Villa a point in the race to finish fifth and a place in next season's UEFA Cup.
The result also ensured that Liverpool can finish no lower than fourth place, the final Champions League berth.
The draw means that Everton has 62 points from 36 games, while has Villa 59 with two rounds to go.
Also, Roque Santa Cruz scored a 74th-minute winner for Blackburn to beat sixth-place Portsmouth 1-0 and virtually end Pompey's chances of finishing fifth.
(Agencies via Shanghai Daily April 29, 2008)