Police are searching the home of a 25-year-old man arrested after the suspected terror attack at Manchester Victoria Station on New Year's Eve.
Assistant Chief Constable Russ Jackson, of Greater Manchester Police (GMP), told reporters at a briefing at force HQ the suspect being held for attempted murder lived in the Cheetham Hill area of the city and officers were at his address.
He said a couple in their 50s suffered multiple stab wounds in the "frenzied" and "random" attack around 9pm.
The suspect was heard to shout "Allah" and "Long live the Caliphate!" during the incident.
Mr Jackson said: "We believe we have identified the man in custody.
"In fact we are currently searching an address in the Cheetham Hill area of Manchester, we commenced that in the last 30 to 40 minutes.
"We know the attacker arrived at the location and soon after he attacked two people, a man and a woman, who have suffered very serious injuries.
"Whilst serious thankfully these are not life threatening."
The BTP said a man and a woman - both in their 50s - were taken to hospital.
The woman has injuries to her face and abdomen and the man has injuries to his abdomen, while a BTP officer has a stab wound in his shoulder.
Their injuries are described as serious but not life-threatening.
A man was arrested on suspicion of attempted murder, officers said.
Assistant Chief Constable Rob Potts said the investigation was being led by counter-terrorism police and officers were keeping an "open mind".
He said: "Tonight's events will have understandably worried people but I need to stress that the incident is not ongoing, a man is in custody and there is currently no intelligence to suggest that there is any wider threat at this time."
The officer, a police sergeant in his 30s, has now been released from hospital, Greater Manchester Police said.
BTP Assistant Chief Constable Sean O'Callaghan said: "I am incredibly proud of the four officers who were immediately on scene last night, detaining a man who was wielding a knife. They were fearless, running towards danger and preventing further harm coming to passengers.
"Unfortunately however, one of our police officers suffered a stab injury to their shoulder and we're all relieved that this is not more serious. It is good news that he has now been discharged from hospital, we are all wishing him a speedy recovery."
Prime Minister Theresa May said: "My thoughts are with those who were injured in the suspected terrorist attack in Manchester last night.
"I thank the emergency services for their courageous response."