The fire broke out on Thursday evening in the former Odeon cinema, Tokyo Jo’s and Evoque nightclub on Church Street.
The building was partly derelict and partly used by businesses at the time.
Two 14-year-old boys have already been arrested and released on police bail, pending further enquiries.
Now police have announced a third person – a 16-year-old boy – was also arrested this morning.
He has also been released on police bail, pending further enquiries.
A joint investigation between Lancashire Police and Lancashire Fire and Rescue Service is underway to establish the cause of the fire.
Road closures remain in place around the building and the area is also closed to pedestrians, as emergency demolition work continues.
Det Insp George Binns, from Preston CID, said: “Three teenage boys have been arrested and all have been bailed while our enquiries continue.
“We are working hard with Lancashire Fire and Rescue Service to establish the cause of the blaze and are still asking anybody with information about it to come forward. Perhaps you were in the area at the time and saw something suspicious, or perhaps you have other information that could help us.
“Whatever you know, we would ask you to get in touch as soon as possible.”
Anybody with information is asked to call 101, quoting log 1347 of May 19th.