Tainton, 35, has worked at Bristol for more than a decade before being made chief operating officer in 2022.
Bristol’s match in Cardiff marks the first time one of their home Premiership matches has been played away from Ashton Gate.
It follows similar initiatives by other clubs to play at international stadiums during the league season, with Saracens playing at the Tottenham Hotspur Stadium and Harlequins at Twickenham during recent campaigns.
Tainton said while there were “no immediate plans” for any games to be played internationally, he “would not rule anything out” in the future.
“What I will say of the Premiership and new executive there, they have come in with a freshness and a purpose and new ideas. I don’t think anything is off the table,” Tainton said.
“We value Ashton Gate and we value our season ticket holders and we value home games – [it’s] certainly not something we’re cooking away in the background in terms of a Premiership game.
“We are very much aligned with Premiership Rugby and their strategy to grow the game to get more eyeballs on rugby.”