The move will allow fans watch in both the Aviva Premiership Rugby match and the England international with South Africa, which will follow straight after, at 2:30pm at Twickenham.
"We know a number of our fans want to see both games so now that can happen," said Gloucester Rugby Managing Director, Chris Ferguson.
"The England match will be shown on the big screens at Kingsholm and on the televisions which are stationed around the ground.
"So, we hope supporters of both teams will turn this into a Super Saturday and watch two cracking matches, back-to-back."
The Gloucester Rugby v Sale Sharks match will also be screened live on ESPN.
Also on the weekend of November 23-25, Sky Sports will screen the trip of champions Harlequins to Bath Rugby, a match that will now kick off at 7.45pm on Friday 23 November.
London Wasps will host Leicester Tigers - also live on ESPN - at 2.30pm on Sunday 25 November.