Investigations at the warehouse could take until the end of January
A fire service could be charged with corporate manslaughter over the deaths of four firefighters, police have said.
Ashley Stephens, 20, John Averis, 27, and Darren Yates-Badley, 24, were found dead in the gutted remains of a warehouse in Warwickshire.
Ian Reid, 44, died in hospital following the fire on 2 November.
Police said Warwickshire Fire and Rescue Service could face charges and they were "ruling nothing out". The fire service has not commented.
Officers have spent the last four weeks searching the shell of the Atherstone-on-Stour warehouse and are treating the blaze as suspicious.
At a news conference held on Wednesday morning, Warwickshire Police said a "meticulous" search of the site had not provided clues to the cause of the fire so far.
Asked whether the fire service would face charges, Det Supt Ken Lawrence said: "It is possible. We are exploring every single possibility and ruling nothing out."
He added: "I still don't know what started it. I am erring on the side of caution, treating it as if it was arson, but clearly I would add that I am open-minded about that."
Dates have now been set for the firefighters' funerals
A fire service spokesman told the BBC it "would be inappropriate" to comment while the investigation was ongoing.
Mr Lawrence said initial reports that migrant workers had been sleeping in the warehouse on the night of the blaze were untrue, although it might have happened on previous occasions.
He added that the search of the site could take at least until the end of January.
Police officers are still interviewing warehouse workers and have drawn up a list of 400 people who were on the site in the days running up to the fire, on 2 November.
Ch Supt Paul Mason Brown, in charge of operations at the scene, said the building was still unstable and the safety of those working there was a priority.
He added that an air raid-style siren was being used to warn people of any movement in the warehouse.
Floral tributes have been laid in front of the site.