In the upcoming second series, the hut will allow two people to get to know each other better away from the gaze of their fellow detainees, although not the millions of viewers tuning in to the broadcasts and webcasts.
It is unclear if the winner of the first series, chirpy Liverpudlian builder Craig Phillips, was asked to tender for the scheme.
Building understands that the hut is being constructed by the In Situ Rammed Earth Company. Rowland Keable, who owns the company, said he was unable to comment on the story because he had signed a confidentiality agreement.
The hut will be completed in time for the screening of the second series later this year.
The building's walls are being constructed from a soil and water mix shovelled between wooden formwork and then tamped down to force air out of the mix – a technique known as rammed earth construction.