Four Vietnamese nationals who are believed to have been in a mill when it caught fire have been named by police.
Officers began searching Bismark House Mill in Oldham after human remains were found by demolition workers last month following a blaze on 7 May.
Greater Manchester Police (GMP) has now named four men who were believed to have been in the mill at the time.
The force said it was keeping an "open mind" about how many people were present and about their whereabouts.
Cuong Van Chu, 39, arrived in the UK in June 2019 and had maintained regular contact with his wife and children until 7 May, but his family had not heard from him since that date, the force said.
Uoc Van Nguyen, 31, was also in regular contact with his wife until 7 May, when he said he was in a mill, police said.
A GMP spokesman added that Duong Van Nguyen, 29, had been in the UK for about a year and last contacted his family about three months ago, when he said he was living in an "abandoned house" and looking for work.
The fourth missing person was named by police as 21-year-old Nam Thanh Le, who arrived in the UK in January and last contacted his family on 4 May when he said he was living in a derelict house in "Dam", believed to be Oldham, and looking for work.
Assistant Chief Constable Rob Potts previously said the force was "particularly interested in hearing from anyone who knows how the building was being used in the lead up to 7 May or who has information about the fire itself".
Det Supt Lewis Hughes said the investigation team were currently following "several lines of enquiry relating to the fire and activities at the mill beforehand".
He said officers were continuing to search Bismark House Mill "to ensure the recovery of all human remains and any objects of significance".
He added that while the force had "reason to suspect Cuong, Uoc, Duong and Nam may have been in the mill during the fire, we are keeping an open mind with regards to how many people were present and their whereabouts".
Since the search began at the site on 23 July, human remains indicating three victims have been discovered, but none of them have been formally identified.
Initially, it was thought nobody was inside the building at the time of fire, police said.
Det Supt Hughes appealed for anyone with information about the men's whereabouts before or after the fire to get in touch with GMP.
"I stress that their safety and welfare is our number one priority."
Debbie Abrahams, MP for Oldham East and Saddleworth, said: "This is a tragedy and my heart goes out to the families who are affected by this situation.
"I'm in close contact with the police, who I know are working incredibly hard to identify the remains found in the mill, and will continue to offer my support to anyone, or any organisation, that needs it as the situation unfolds."