Savage knows the locals have been itching to see the elite back in the city and he expects an even more intimidating atmosphere than normal when Perpignan, Edinburgh and Munster try their luck on their travels.
"The fanbase we've got is absolutely phenomenal. I don't think you can beat the atmosphere: there's not an atmosphere in England like it," said Savage.
"We know that and the players thrive off that. It's a really tough place to come and if we can make it as tough as possible then it will be hard to be beaten there. That's something we'll concentrate on.
"We've got to focus on our home games, and anything you can pick up on the road is a bonus. There will be a massive emphasis on the home ties given how difficult it is to come to Kingsholm.
"The Heineken Cup is massive for us. We worked hard to get back in there. Historically we've often been in the Heineken Cup and it's massive for the fans. It's something that the city needs."
Gloucester kick off their Pool 6 campaign at home to Catalans outfit Perpignan on Saturday evening, with Savage keen for his side to start with a bang in what could be a particularly tight group.
The fact that the visitors will arrive in the West Country with former Gloucester back rowers Alastair Strokosch and Luke Narraway in their ranks is set to add to what should be another exciting European occasion at Kingsholm.
"There are a few ex-Gloucester players who are in that Perpignan side so they'll be looking forward to coming back," added Savage.
"I'd imagine the banter will begin to pick up now. Some of the boys are in good contact with those two lads. I got on with them really well while they were at Gloucester - they helped me come through some I'm really looking forward to playing against them.
"Stroks was here for a number of years and Naz was here for just shy of 10 and was captain so that adds an extra bit of spice to it. He's going to be telling his boys what to expect so there's certainly going to be an extra edge to the game."