Fire crews were called to Special Ops Desert Storm building in Borough Road around 5pm on Monday (3 July). A nearby factory had to be evacuated as firefighters tackled the blaze.
Merseyside Fire and Rescue Service said: "Fire Crews arrived to find a large building with an area of around 20 by 30 metres well alight. There have been reports of two people who have entered the building and have not yet come out."
The service said part of the building's roof had collapsed and a "large quantity" of tyres were also on fire, Sky News reported.
Witnesses described how half of the building was destroyed and that dark plumes of smoke were seen from miles away, with one social media user saying the smoke could be seen from North Wales.
Sue Clark was on a Ryanair flight from Cork to Liverpool when she saw grey smoke billowing from the site.
She told the Liverpool Echo: "The whole plane was looking out the window as the sky and clouds were completely black. The fire looked to be absolutely huge and the pictures don't do it justice.
"The pilot went a different way round as well to avoid it."