So far, the local Bud distributor has made the highest offer for the naming rights.
But there are some legal issues and concerns.
Harris Wholesale is willing to pay the city of Raleigh at least a total of $1.5 million over the next 5 years.
At a news conference Monday, Mayor Charles Meeker said he doesn't think the deal would make the city look bad.
"We've been recognized as one of the most wired cities, educated cities, best places to work and live and the like. We got there because the community is different. It's a younger community people are accustomed to going out where alcoholic beverages are served. Things may have been different 20 or 30 years ago but now we really are a 21st century city. Something like a beer name is not out of place in our community," he offered.
Meeker says the offer, if it's deemed legal by the state ABC board and the city council, would end up covering about 75 percent of the cost to build the amphitheater.
But some residents have concerns.
"It's good to help with the money but at the same time, Budweiser? You know, do you want to take your kids to a Budweiser Amphitheater? I don't know," said Anita Smith
Others think it's a good idea.
"I personally wouldn't really have a problem with it. I can see why some people do, but personally I don't have a problem," said John Haygood.
"You see it in the Super Bowl and that, so it's not really going to make a difference," explained Amanda Klusmeier.
Named or not, the amphitheater gates will open June 4 for a free concert with The Connells.