And while Triple-A's Zach Davies -- who pitched at this year's Futures Game -- is a name that has surfaced, it's expected to take much more for the Brewers to part with Parra before Friday's 4 p.m. ET non-waiver Trade Deadline.
"He's been a pretty good player. Ben Zobrist brought two players back," Melvin said, referring to the A's sending Zobrist to the Royals for Minor Leaguers Aaron Brooks and Sean Manaea. Manaea, a left-hander, is a top prospect.
"Gerardo's had a better year than Zobrist but Zobrist has had a better career," Melvin said.