"I think people know that," Melvin said Thursday.
Melvin confirmed Greinke's availability in comments to USA Today and Milwaukee's WTMJ radio earlier Thursday.
Melvin did not go into detail on how many teams have expressed interest in the 2009 AL Cy Young Award winner, saying only that the trade market always heats up with the July 31 non-waiver trade deadline approaching.
"I'm very fond of him," Melvin told USA Today. "He's one of my favorite players I ever had. Really, he's been like a son to me. I enjoyed talking baseball with him. He's very passionate. He follows the game. It's been a great experience having him for a year and a half.
"There are so many good things about him, it's going to be difficult when we trade him."
Greinke is scheduled to pitch Sunday's game against Washington at Miller Park, but Nationals manager Davey Johnson said he'd be surprised if that happens.
"I'd be real surprised," Johnson said. "If a ballclub's intent on making a move, they're not going to pitch him two days before the deadline. That's probably why they've got eight pitchers in the bullpen. I'm surprised he's still here."
Despite losing Prince Fielder to free agency in the offseason, the Brewers expected to be contenders in the NL Central again this season. Instead, they enter Thursday night's game against the Nationals 9½ games behind the division-leading Cincinnati Reds.
Melvin said he never expected to be talking about trading away one of his top players at the deadline.
"I didn't think so," Melvin said. "Didn't plan on it."
Greinke is 9-3 with a 3.44 ERA this season.
He pitched three straight starts for the Brewers around the All-Star break -- he was ejected in the first inning of a July 7 game at Houston, started again the next day and then pitched the Brewers' first game after the break.
The team then scrubbed Greinke from his next start, saying the odd stretch of starts had taken him out of his routine and worn him down.
Greinke returned to the mound in Philadelphia on Tuesday, giving up a run and three hits in seven innings -- but the Brewers still found a way to lose the game.
Manager Ron Roenicke said Greinke didn't seem to be distracted by the trade talk.
"It didn't seem to affect him in his last outing," Roenicke said.
Catcher Jonathan Lucroy, who returned Thursday night after missing 50 games with a broken bone in his right hand, said he was surprised Melvin acknowledged he was shopping the right-hander.
"Obviously, with Doug, there's a method to the madness and Doug knows what he's doing," he said. "So if trading Zack means helping us as a team and an organization that's what he's going to do."
Lucroy said he's talked to Greinke about the situation.
"We talk a lot," he said. "He likes it here -- loves it actually. It's his kind of place to play. His wife likes it here, too.
"Obviously, baseball's a business and Zack understands that part of it more than anybody," he said. "He's going to be OK with it. Absolutely he could come back (and re-sign with the Brewers in the off-season.)"
Milwaukee is returning home Thursday night after an 0-6 road trip.
Information from The Associated Press was used in this report.