Lueck, who is from El Segundo, California, vanished within hours of arriving at the Salt Lake City airport on June 17 from a trip home for her grandmother's funeral.
Brown said cell phone records show both Lueck and Ajay's phones were at the park at about the same time.
"This was the same time as Mackenzie's phone stopped receiving any further data or location services", Chief Brown said.
Ajayi's arrest came as police discovered he was the last person Ms Lueck communicated with, police searched his home on Wednesday and Thursday.
It's not clear if investigators have recovered those items.
Investigators found charred material that were determined to be human female tissue that matched Lueck's DNA. Ayoola Ajayi was arrested on Friday and charged with the murder of MacKenzie Lueck after officials were able to determine that the "charred remains" found in the suspect's back yard belonged to the 23-year-old college student.
He was arrested earlier Friday morning by a SWAT team.
Brown said that the woman's remains and some of her possessions were found burned in the backyard of Ajayi's residence. She was then taken to Hatch Park at 2:59 am local time, according to the SLCPD.
His neighbor, Tom Camomile, told CNN prior to Ajayi's arrest that he was a "smart guy" and a "computer geek".
Here's what you need to know about the case.
Mackenzie Lueck, 23, is seen leaving the departure area at Salt Lake City International Airport.
Airport surveillance footage showed her rolling her luggage through the airport in the early morning hours.
Salt Lake City Police requested for the person who picked up the items to contact them, as they continue searching for Lueck.
The Lyft driver told police that Lueck did not appear to be in distress. (He also denied meeting with her at anytime.) The police did not specify if Lueck knew Ajayi before this text conversation, or offer any details on the nature of their conversation.
CNN has reached out to the US Army and Dell for comment. An account bearing the name "Kenzie Lueck" followed another Instagram user on or about Wednesday, CNN verified. - Family notifies police that Lueck had not been heard from since Sunday night.
Investigators have been looking into the account's activity, along with the rest of the case's "digital footprint", Brown confirmed Thursday.
"This is one of the most hard phone calls I've ever made", Brown said. They said they were also looking for a mattress and box spring removed from the home last week.
Lyft also issued a statement to media outlets.
"As a mother and a mayor, my heart breaks for the Lueck family". "She would never miss her midterms or anything like that". It was initially thought she caught the Lyft vehicle home. "She didn't show up to work, or anything".
Authorities are filing murder and kidnapping charges in the death of a Utah college student who disappeared 11 days ago. Her friend Juliana Cauley said "it's been extremely hard". "On behalf of the university, I express our heartfelt sympathy to the family, friends and classmates of Mackenzie during this very hard time".