The 48-year-old Melvin, who won the NL West title with Arizona in 2007, has had a phone interview for the Toronto Blue Jays job this offseason and also interviewed for the Chicago Cubs opening. That job went to Mike Quade, who had taken over for Lou Piniella on an interim basis in August.
The Brewers are expected to name a manager by the beginning of next week. They did not exercise their option on Ken Macha at the conclusion of the regular season.
Milwaukee also has sought permission from the White Sox to speak with Joey Cora, Chicago's bench/third base coach.
Tim Kurkijian covers Major League Baseball for ESPN and ESPN The Magazine.