"I don't think there's any secret, with the Trade Deadline, that this is a possibility," Melvin told MLB.com's Adam McCalvy. "Zack knows that. We know that. Other teams know that. He's the best pitcher out there. A guy that could be a difference-maker. There are teams that understand that."
There are other pitchers who could be available, including Rays right-hander James Shields and Marlins right-hander Josh Johnson. But they are not considered in the same stratosphere as Greinke, who is 9-3 with a 3.44 ERA in 21 starts for the Brewers.
He is scheduled to start on Sunday for the Brewers, but there are indications that something could get done before then. If the Rangers could get something done by Sunday, Greinke could conceivably start on Monday in the first of a four-game series with the Angels at the Ballpark in Arlington.
There are other teams interested in Greinke and the competition could get fierce. The Braves and the Angels are reportedly interested in Greinke and the Dodgers have been actively trying to acquire pitching. Other teams could emerge as the Deadline approaches.
The Rangers have an advantage simply because they have one of the deepest farm systems in baseball. The crown jewels of the system are pitcher Martin Perez, infielder Jurickson Profar and third baseman Mike Olt, and there is little doubt the Brewers would covet at least one of those three. That would also be just a starting point.
If the Rangers acquired Greinke, they would be getting a pitcher who will be a free agent at the end of the season. Under the new CBA rules, the Rangers would not get compensation if Greinke signed with another team.
The possibility of getting Greinke as nothing more than a rental player is unlikely to deter the Rangers. It may mean they are willing to give up less for him, but the Rangers are in a "win-now" mode. After losing two straight World Series, it's quite clear what the Rangers' goal is this season, and general manager Jon Daniels can get quite aggressive around the Trade Deadline.
"As players, we want to get someone that can help the team," third baseman Adrian Beltre said. "We might need a starting pitcher now that Colby's out for the season. We don't know. There's nothing we can do about it. I don't really tweet but I see what's going on sometimes."
The Rangers' rotation is currently led by right-hander Yu Darvish and left-handers Derek Holland and Matt Harrison. Roy Oswalt, who was scratched from his last start because of tightness in his lower back, is scheduled to return to the rotation on Sunday.
He will be followed on Monday by Scott Feldman, who has shuttled back and forth from the bullpen to the rotation, and is riding a four-game winning streak. Neftali Feliz, who has been on the disabled list since mid-May with a sprained right elbow, has made three starts on rehab assignment and is scheduled to pitch again on Sunday for Triple-A Round Rock against Memphis. He will likely need one more start after that.
The Rangers have also discussed the possibility of shifting Alexi Ogando to the rotation. He was a 13-game winner as a starter in 2011 before returning to the bullpen this season.
But their first option right now is to explore ways of bringing Greinke to Texas. The non-waiver Trade Deadline is 3 p.m. CT on Tuesday. Greinke is scheduled to pitch on Sunday. Or maybe it will be Monday.