Japan is prepared to phase out tariffs on hard cheeses such as cheddar by 2033, but is refusing to go soft on fresh and blue-veined varieties, which would have duty-free access on an agreed quota by the same date, the Financial Times reported.
Truss holds Stilton close to her heart and it has appeared in many of her most prominent public speeches in the past.
The UK has been keen to sign a quick new deal with Japan and advance the UK's accession to the Comprehensive and Progressive Trans-Pacific Partnership, a move which would improve market access for UK businesses across the Asia-Pacific region.
The talks involve around 100 negotiators from the UK side taking part in negotiations by holding video conferences with their Japanese counterparts every day.
UK trade with Japan was worth more than £30 billion last year, with 9,500 companies exporting goods to the Asian country, according to Government figures.
Government analysis suggests a free trade agreement between the UK and Japan would bring greatest benefits to Scotland, London and the East Midlands.
