A police officer was injured during Friday's raid on the four-storey building in Bangkok, where guns and drugs were also found.
Thai police suspected the building in the Phra Kanong district was being used as a passport-forging operation.
The UK Foreign Office said it was looking into reports that one of the men could be British.
"We are seeking further information from the local authorities following reports that a British national has been arrested in Thailand," a spokesman said.
