The Brewers have been the Sounds' parent club since 2005 and recently extended their player development two more years, through 2014, while noting their dissatisfaction with Greer Stadium, which will turn 35 next season.
"The problem is, there's nothing ever open. Everybody gets locked in," Melvin said. "It's the same at [Double-A] Huntsville."
Greer Stadium was already 10 years old when Brewers manager Ron Roenicke played there in 1988 as a Cincinnati Reds farmhand.
"They could have used a new stadium then," Roenicke said.
He would love to see a deal get done so the Brewers can remain in Nashville.
"You get a new stadium, great baseball city," Roenicke said. "It really is. I had a great time there."
Tuesday's report in the Tennessean came a year after an independent commission identified three sites for a new stadium in Nashville.
"This could be a good baseball town," Melvin said. "If they built a new ballpark down by the football stadium, they'd draw people."