Bradford chairman Mark Lawn says the fan arrested for allegedly racially abusing Reading winger Garath McCleary faces a lifetime club ban.
McCleary made the complaint just before half-time, at which point a supporter was arrested and ejected from the ground by police.
"I heard about that and when we find out who it was we will take action," Lawn told Press Association Sport.
"I understand the police are prosecuting so we can't do anything at this stage, but if that person is found guilty we will take action.
"There is no place for that in the game, it is unacceptable.
"I would think we're looking at a lifetime ban if he's found guilty but that decision can only be made after consultation with the club's board."
The Football Association will contact Reading and Bradford to seek their observations following the pitch invasion after Monday's FA Cup quarter-final replay at the Madejski Stadium, Press Association Sport understands.
Reading fans ran onto the pitch after the final whistle in their 3-0 win over the Bantams which secured an FA Cup semi-final clash with Arsenal at Wembley.
A supporter also invaded the playing surface during the game and the FA will speak to both clubs to collect their views.
Garath McCleary was the target of alleged racist abuse during his side's 3-0 win over Bradford.
The winger reported an incident to the assistant referee after he'd gone to collect the ball to take a corner just before half-time.
Reading confirmed they had reported the matter to the police. who confirmed a man gad been arrested.
An incident was reported to the match officials just before half time, who in turn told Reading staff. A man was then arrested and ejected during the half-time interval.
Reaching an FA Cup semi-final will be a bigger achievement than making it to the League Cup final, according to Bradford City boss Phil Parkinson.
The Bantams take on Reading for a place in the final four, which could see Parkinson and his men return to Wembley, having made it to the League Cup final in 2013.
"The FA Cup is obviously a level above the Capital One Cup. If we can do it this time it will be the first time since 1911 and this group of players will be remembered.
"This is what being involved in football is all about, and the big teams from the Premier League will be casting very envious eyes on ourselves and Reading playing in an FA Cup quarter-final on Saturday."
League One Bradford claimed another Premier League scalp to book their place in the FA Cup quarter-finals for the first time in 39 yearsRead the full story ›
After beating Chelsea in the fourth round, Bradford have done it again in the fifth, beating Premier League side Sunderland 2-0 at Valley Parade to progress to the FA Cup last eight. The match was not televised live, to the dismay of many supporters.
Another marvellous effort from Bradford City. FA Cup quarter finalists.
The TV companies cant ignore Bradford any longer. All the QFs are all on live with £250k each for the eight teams.
Bradford are at it again, taking a 1-0 lead over Premier League opponents Sunderland at Valley Parade, with only three minutes on the clock. Billy Clarke appeared to be the scorer, but Black Cats defender John O'Shea might yet be credited with an own goal.
Bradford City co-chairman Mark Lawn says he would like to face Manchester United in the FA Cup for his wife Yvonne who is battling cancer.Read the full story ›
Bradford City manager Phil Parkinson hopes his side's victory over Chelsea will be rewarded with a trip to Old Trafford.
Manchester United still need to get the better of Cambridge United in a a replay following a 0-0 draw on Friday in order to join the Bantams in the hat.
If I had my choice, I'd like to play Manchester United.
The experience we had yesterday going to Old Trafford was just terrific. If Manchester United can manage to beat Cambridge it would be great to go to Old Trafford.
But whoever we get, it's great to be in the fifth round. We're enjoying being in the limelight.
Bradford City goalkeeper Ben Williams has praised the conduct of Jose Mourinho after Chelsea were defeated by the League One side.
The Portguese manager went in to the visiting dressing room, after his side were humiliated 4-2 at Stamford Bridge, to congratulate the Bradford team.
"It was fantastic. The scenes, the look on everyone's faces was amazing, something which will live long in the memory," Williams told BBC Radio Five Live's Sportsweek programme.
"The fans were amazing and after that Mourinho came into the dressing room and shook everyone's hand and congratulated us, that was a surreal moment as well.
"In he walked and the celebrations stopped. This figure waltzed into the dressing room. He was very classy, very humble, very respectful - it was the icing on the cake."