Fellow finalists Canberra, North Queensland, Brisbane, Penrith, Canterbury and Gold Coast are also not keen.
"It's a long way to go for a game that doesn't mean anything," Cowboys football manager Peter Parr said.
Sydney Roosters' participation in the 2016 series in February, where they beat St Helens 38-12, may back up the clubs' concerns about player burn-out close to the season opener.
The 2015 minor premiers lost the first eight games of the season, although they had other contributing factors to their poor start following Mitchell Pearce's Australia Day antics.
Fellow participants Brisbane and North Queensland fared considerably better, with the 2015 premiers winning three of their five first starts and the Broncos four.
- AAP