The 23-year-old England international announced that he would be leaving Gloucester at the end of the season, with Leicester Tigers his supposed suitors, but he would love nothing more than to bow out with a trophy in his hand.
"It would mean a massive amount to me to finish with some success. I'm not lying when I say I love this club and love playing for them," said Burns.
"I feel the time is right to move on but I'll treasure the last few games I have for Gloucester. It's always exciting to be in a quarter-final, whether it's the Heineken Cup or the Amlin Challenge Cup. I'm confident I can put in some good performances for the rest of this comp.
"I had a good performance on Sunday and I'm excited to be here with a great young squad and (I'm looking) to put in a performance at Kingsholm on Saturday."
Burns was just one of a number of standout players on Sunday, with Jonny May scoring a sensational solo try from fully 80 metres early in the first half and wing Shane Monahan grabbing a brace of scores as Gloucester gained the bonus-point win they needed to pip Cardiff Blues to a quarter-final spot.
No8 Gareth Evans was another in fine form at the Stade Aime Giral as his took his starting chance with both hands with England international Ben Morgan on the bench. As well as carrying well throughout and proving solid in defence in the south of France, Evans' set up Charlie Sharples' try with an incredible burst of pace from inside his own 22.
"Days like Sunday are what you live for as a rugby player," Evans told the Gloucester Citizen.
"I love having the ball in space. The guys take the mick out of me saying I'm a failed back but if I get myself in those wide channels I will have a go.
"I had (Charlie) Sharples, and I think (Jonny) May, on the outside and you know if worst comes to worst you can just give the ball them and they will do something. But I gave it a go and it came off."