Joe Cole and Rufus Brevett will not face criminal charges following the incidents after West Ham's Premiership game with Bolton at the Reebok Stadium last month.
In a stormy encounter, which Bolton won 1-0, West Ham's Ian Pearce was sent off for a foul on Pierre-Yves Andre and tempers later flared after the final whistle.
There was a melee in the centre circle and the bad feelings continued in the tunnel as the players left the field.
A police investigation was carried out and a report will now be forwarded to the English FA.
The FA was awaiting the police response before deciding whether to take action themselves.
Cole and Brevett could face a misconduct charge although there is believed to be a problem gathering evidence because it is understood referee Uriah Rennie did not see any trouble in the tunnel. But the FA could act on evidence from stewards and the police report.