Utley, who has cleared waivers, would have to be traded before the Aug. 31 deadline to be eligible to play in the postseason. He has a full no-trade clause in his contract.
"As I told you before, it is very likely he'll be here in Philadelphia through the end of the year, and then we'll see what happens after that," Amaro told 94WIP in Philadelphia.
Amaro declined to comment when asked whether Utley was limiting where he would be traded or whether the offers the Phillies have received weren't enticing enough to seek Utley's approval.
Later Tuesday, Amaro said he thought the Phillies wouldn't trade Utley as far back as 2014, when Utley earned his 10/5 rights (10 years in the majors, five with the same team) and could veto any trade.
"I don't feel Chase has a desire to leave Philly. And the Phillies don't have a desire to move him out of here," Amaro said. "But like I've said, we're still open-minded. We're not in a mindset to move him. We're not in a mindset to keep him. We're just open-minded."
Asked whether he would consider it a lost opportunity if the Phillies don't trade Utley this month and then get nothing in return at the end of the year when Utley is likely to become a free agent, Amaro said: "I don't think it's a lost opportunity necessarily. We've got to assess a lot of different things about him being here. There's a lot of positives to having Chase Utley still in our uniform."
After going 2-for-5 in Tuesday's 8-5 loss to the Toronto Blue Jays, Utley is 15-for-31 at the plate since coming off the disabled list Aug. 7. Amaro said this was a clear indication that his longtime second baseman is far from finished.
"He's moving well," Amaro said. "His bat speed is very good. You can see his legs are underneath him. And it seems pretty clear that there was something going on in his ankle that was limiting him in some way, shape or form. He looks like he's pretty much a man on a mission."
ESPN.com's Jayson Stark contributed to this report.