It is understood the 32-year-old was an asylum seeker from the Middle East who converted to Christianity in 2017.
Police say "important evidence" has been found at an address he rented.
In an update on Monday evening, Assistant Chief Constable Russ Jackson, head of Counter Terrorism Policing North West, said the property at Rutland Avenue near Sefton Park, in the south-east of the city, was "becoming central to the investigation".
It could take weeks to establish how the incident was planned and prepared.
Four men were arrested in the Kensington area of Liverpool - three aged 21, 26 and 29, who were held on Sunday, and a 20-year-old man who was detained on Monday.
ACC Jackson said: "Following interviews with the arrested men, we are satisfied with the accounts they have provided and they have been released from police custody."