The Football Association has contacted both clubs after a pitch invasion by Aston Villa fans during Saturday's FA Cup quarter-final win over West Brom.
Some Villa supporters ran on to the Villa Park pitch in injury time and at full-time, while seats were thrown from the stand housing West Brom fans.
The FA described the crowd trouble as "disturbing" and said offenders will face "appropriate punishment".
Villa won the match 2-0 to secure their first Wembley appearance in five years.
Captain Fabian Delph and winger Scott Sinclair scored the goals, before the game was marred by events around the final whistle.
Referee Anthony Taylor was forced to halt the game in stoppage time as home fans spilled onto the pitch.
The match resumed after a short delay, before another invasion after the final whistle.
Villa issued a statement on Monday saying the club would "co-operate fully with the Football Association".
The FA said: "As well as liaising with both clubs, the FA is working closely with West Midlands Police and notes that a number of arrests have already been made.
"All available video footage will be studied by the relevant parties to identify anyone who has committed a disorder offence inside the stadium and ensure they face the appropriate punishment."
West Midlands Police said it would support the FA in identifying the people involved.
Four arrests took place at Villa Park - one man for being drunk entering the ground, another for failing to comply with a football banning notice and two for public order offences.
Cheshire Police's Mark Roberts, the national lead officer for football policing, questioned playing the tie at 17:30 GMT.
"They are big clubs, not clubs that particularly have a troublesome following. But when you have that sort of fixture, late on a weekend in particular, alcohol is a factor," he told BBC Radio 5 live.
"If you give people four, five, six hours' more drinking time, don't be surprised if in a highly-charged atmosphere, their behaviour isn't good."
West Brom expressed their "deep concern" that the safety of players and staff was "clearly compromised".
Baggies boss Tony Pulis called the scenes "disgraceful" and, asked about reports of away fans ripping up seats, said: "Those supporters should never come into another football ground."
Football Supporters' Federation chief Malcolm Clarke believes talk of lifetime bans is "over the top".
"You have got to have punishments which are proportionate to the offence," he added.
"The law at the moment has a maximum 10-year period for a football banning order, so it would be rather odd for people to start talking about lifetime bans."
A West Brom statement said the club received Aston Villa's apology for the "disturbing scenes" during and after the match "in the spirit with which it was intended".
It said: "The club is also aware of reports of serious misbehaviour involving some of its own supporters.
"It issues an uncompromising reminder that any supporter found guilty of disorder offences can expect the appropriate sanction from the club."
The FA has not set a timeframe to conclude the investigation.
Possible sanctions against Villa include a heavy fine for failing to control their supporters.
West Midlands Police is also investigating a pre-match disturbance at a pub near the ground after 13 men were arrested on suspicion of various public order offences. Three have since been charged.