"Successful firefighting tactics have resulted in the fire being greatly reduced," Merseyside Fire and Rescue Service (MFRS) said.
The main body of fire has been extinguished.
Twelve fire engines rushed to Fox Street in Liverpool after the blaze broke out at about 14:20 GMT.
MFRS said there had been no reports of casualties and more than 50 firefighters attended the blaze at its height.
It said neighbouring properties had been evacuated as the building was in danger of collapsing.
Nearby roads were temporarily closed by police but Great Homer Street has now been reopened for vehicle access.
MFRS has earlier declared the incident a major incident and that the fire had been "divided into four sectors, with ground monitor main branch hoses, multiple main branch hoses and a combined platform ladder in use".
It said Merseyside Police were assisting with the evacuations and a cordon was in place around the building and the wider area.
People were warned to avoid the area and local residents have been told to shut windows and doors.
Huge plumes of smoke could be seen across the city, including over Goodison Park during Everton's FA Cup tie against Luton Town, as well as from across the River Mersey in Wirral.
MNA
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