Licensing officers will ask for immediate measures to be implemented to ensure public safety and will examine whether the club should be stripped of its permission to sell alcohol and whether the supervisor should be removed.
Crane previously expressed condolences for Mr Fisher’s family and cancelled its New Year’s Eve event out of respect for them.
Responding to a review of its licence on Thursday, a spokesperson for Crane added: “An expedited review of a premises licence is normal whenever any serious crime takes place at a licensed premises, and we are cooperating fully.
“We place the highest priority on all aspects of public safety and security.
“Whilst it would be wrong for us at this stage to react to individual, anecdotal accounts of the circumstances that applied on Boxing Day, we do employ extensive and professional security procedures for all public events, and our contracted security staff are professionals who are licensed by the SIA.
“But we will of course be conducting a full and detailed review in light of this week’s tragedy, as well as assisting fully with the ongoing police enquiry.”
Officers said they arrested a 22-year-old man in London at around 3am on Thursday in connection with the stabbing.
He is the third person to be arrested on suspicion of murdering Mr Fisher, while four others have been arrested on suspicion of assisting an offender.
Police recovered a knife from the crime scene and a post-mortem examination has confirmed that Mr Fisher died of a stab wound.
Detective Chief Inspector Ian Ingram, leading the investigation, repeated the plea for anyone with information to contact police.
He said: “We now have seven people in custody and continue to build a picture of the events that led to the tragic loss of this young man’s life.
“People are continuing to come forward with information, but I still want to hear from anyone who has not yet got in touch with us.
“If you have footage that we have not yet seen, or you know what may have happened in the lead-up to Boxing Day’s awful events, I’d urge you to do the right thing and speak to us right now.
“We are determined to get answers and justice for Cody’s friends and family, and won’t stop until that happens.
“We are keeping them updated with developments as they happen, and continue to support them through this awful time.”
Police arrested a 22-year-old on suspicion of murder in Birmingham city centre just after midnight on Wednesday, while a second man, aged 21, was arrested for the same offence several hours later in London.
Mr Fisher was remembered by his girlfriend, Jess Chatwin, in an emotional message posted on Twitter the day after his murder.
She wrote: “You didn’t deserve any of this. I’m so sorry this has happened to you my baby please come home. I love you forever Cody Fisher.”
A statement published by the police and attributed to Mr Fisher’s family said: “They have broken our hearts; I have lost my best friend. My family and I are asking for privacy and respectfulness at this heart-breaking time.”