The 27-year-old has become an England regular since joining
Wasps in 2013, winning 17 caps since making his debut in 2016, but it appears Bristol's big bank account will ensure the deal goes through.
Hughes, who currently earns between
£250,000 and £300,000, is currently on holiday in Dubai this week with a source close to the player revealing to the Mail that he has not made a decision about his future.
Premiership clubs are not allowed to approach players contracted to another club until January 1 of the year their deal expires.