Supt. Bob Hassel told a news conference Monday he couldn't say more to protect the integrity of the investigation.
Travis Brandon Baumgartner, 21, is in custody in Langley, B.C., where he appeared before a justice Sunday night. Baumgartner was caught a day earlier trying to cross the border.
Hassel said it's hoped Baumgartner will appear in court in Edmonton as early as Wednesday, but it could be any time within the next six days.
He also said Matthew Schuman, a fourth guard badly wounded in the shooting Friday at the University of Alberta, was improving somewhat, although he remained in critical condition.
The president of security company G4S Canada also appeared at the news conference and said a fund has been set up to which the public can contribute to support the families of the victims.
But Jean Taillon wouldn't take any questions. He said the company wants to focus on its internal investigation. G4S has flown out its own security experts to conduct that review.
Taillon did not address how G4S employees are screened.
A Facebook page of a Travis Baumgartner had quotes from the villainous Joker in the "Dark Knight'' movie, which included a violent bank heist. It also mentioned "popping people off" to make the six o'clock news.
"I cannot begin to describe the shock and grief the G4S family is still feeling after the tragic event on Friday," Taillon said.
"We lost three valued members and another remains in critical condition in hospital. Our thoughts and prayers remain with their family and friends and we will do everything we can to help and support these families through difficult times.
"Our thoughts are also with the Baumgartner family."
Police are still looking for the work pistol and bulletproof vest they believe the suspect had with him at the time of the shooting that left Eddie Rejano, 39, Michelle Shegelski, 26, and Brian Ilesic, 35, dead.
Police have said Baumgartner was on an overnight crew of five that was reloading an ATM at the university's HUB mall and residence shortly after midnight Friday.
An armoured car was found later that day halfway across the city. It was still running with its lights on.
Baumgartner was first named a person of interest, but that was upgraded to a suspect just a few hours later. Police issued warrants for his arrest on three counts of first-degree murder and one count of attempted murder.
Hassel said investigators are attempting to track Baumgartner's movements between Edmonton and the border.
Baumgartner tried to get into Washington state Saturday afternoon at a border crossing just north of Lynden, Wash., near Abbotsford, B.C.
Police say he was driving the same dark-blue pickup truck investigators had been looking for with an Alberta licence plate belonging to his mother on the back.
He had no passport, just a driver's licence that police had flagged in their computers.
They say there was a backpack with $330,000 in the truck.