His general manager responded Friday, saying he had "no desire" to trade Lee -- or fellow pitchers Cole Hamels and Jonathan Papelbon, for that matter.
Amaro was just as adamant that it was illogical for the Phillies to consider trading Papelbon. The 32-year-old closer is in the second year of a four-year, $50 million contract that contains a vesting option for 2016.
"People would like us to improve our club, but at what cost?" Amaro said. "You have to have replacement pieces if you're going to trade someone like that. And we don't have a guy who I consider a closer on our club other than Papelbon. He's the best we've got and one of the best in baseball, if not the best.
"I believe you have to have a closer to win and have success, and I believe in having a [true] closer. Not a closer by committee. A guy who stops the game when you're supposed to win late. We don't have a replacement to do that. ... And I don't see any closer on the market who would be anywhere near as good as Papelbon. I just don't see it. So if you want to win, why would we want to trade a guy like that?"
Amaro's remarks came one day after Lee and the offensively challenged Phillies barely won a 3-2 game in Minnesota despite outhitting the Twins 16-3.
Afterward, Lee danced away from multiple questions from the media about whether he wanted to stay in Philadelphia.
Here is how a portion of that Q-and-A went, according to CSNPhilly.com:
Q: "If it doesn't turn around, do you want to stay?"
A: "I definitely want to win. There's no doubt about that. I want to win. I don't know how to say it besides that. I want to win."
Q: "If it doesn't turn around, are you prepared to stay here for two months and play out the string?"
A: "I don't have any control over that. I know that I want to win, and I'll voice that to whoever. And that's that. I want to win here. That's why I signed here, and that's where my focus is."
Amaro said he empathized with Lee, who had the seventh-worst run support in the National League last year and has seen the Phillies score three runs or fewer in eight of his 14 starts this year, but only to a point.
"I feel the same way," the GM said. "I just want to win too."
But Amaro, whose team is three games under .500 (32-35) and 7½ games out of first place in the NL East, went on to say that even if the Phillies don't play their way into contention over the next month, he wants to build around Lee and Hamels, not trade them.
"My job is to try and put a contending team on the field every year, and we have a much better chance to be a contending team with both of those guys on the club," he said. "If we have those guys at the top of our rotation, we're a better club. ... It starts and ends with pitching, as far as I'm concerned. So the more quality pitching you have, the better chance you have to build around that to win."
Amaro said he "understands Cliff's frustration" about the team's record and lack of offense. But the GM said Lee's hints about wanting to leave are "not really a factor" in the club's thinking.
"He doesn't have a 'trade-me' clause," Amaro said. "So while I understand that he wants to play for a winner, I think we can provide that for him in Philadelphia."
Amaro also dismissed, for the second time in a week, the idea that the Phillies need to blow up their team to get back into contention, in either the short haul or long haul.
"Whether you're talking about retooling or rewrapping or taking a different direction, I think there are ways we can do that," he said. "But when you start talking about blowing it up, you're basically saying you're going to start from scratch. And that's not happening."
Even if the Phillies decide to sell and commit to holding onto their pitching, "We have plenty of people to trade," Amaro said. He also said he thought his team would have significant payroll flexibility after this season, when "four or five guys come off the payroll."
Chase Utley, Carlos Ruiz, Roy Halladay and Michael Young -- four players whom the Phillies will pay a combined $46 million this year -- will all be free agents after the season. And that, Amaro said, "will give us the ability to figure out what we want to do, whether we want to utilize those dollars to re-sign those players or utilize those dollars to bring someone else in here to help us win."
But Amaro said he saw no reason the Phillies would have to move one of their high-paid starters to create even more flexibility.
"I have no desire to trade those guys," he said, then added, "At all."