Greater Manchester Police has now released the pictures of Cuong Van Chu, Uoc Van Nguyen, Duong Van Nguyen and Nam Thanh Le, who were reported missing on July 21.
Cuong, 39, who arrived in the UK in June 2019, maintained regular contact with his wife and children, but they have not heard from him since May 7.
Uoc, 31, also kept in contact with his wife but she has also not heard from him since May 7, at which time he said he was in a mill.
The third man, 29-year-old Duong, arrived in the UK approximately 12 months ago.
He last contacted his family roughly three months ago, at which time he said he was residing in "an abandoned house" while looking for work.
After arriving in the UK in January this year, Nam, 21, last contacted his family on May 4.
At the time he said he was residing in "a derelict house" in ‘Dam’, believed to be Oldham, while searching for a job.
Teams began searching the remnants of the mill after demolition workers discovered human remains on July 23.
Initially, it was thought nobody was inside the building at the time of fire, said police.
But now, specialists have confirmed the recovery of remains of three victims, though they have not yet been formally identified.
Detective Superintendent Lewis Hughes, GMP’s Victim Identification lead, said: “Our thoughts remain with Cuong, Uoc, Duong and Nam’s loved ones.
"Specially-trained officers have been in direct contact with them and continue to make every effort to ensure they are fully updated and supported in Vietnam, as they would be in the United Kingdom.
“We are continuing to search Bismark House Mill to ensure the recovery of all human remains and any objects of significance. Meanwhile, the investigation team is following several lines of enquiry relating to the fire and activities at the mill beforehand.
“Though we have reason to suspect that 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.
"I, therefore, appeal to them or anyone with information about their whereabouts before or after the fire to contact us. I stress that their safety and welfare is our number one priority.
“We also continue to appeal for information about the fire or activities at the mill beforehand.”
Anyone with information has been urged to contact Greater Manchester Police on 101 quoting Operation Logan, or get in touch anonymously via Crimestoppers on 0800 555 111.