The Astros could have traded Qualls prior to the non-waiver Trade Deadline but weren't in a hurry to move their most effective reliever, especially considering he's under contract for next season. Qualls wants to end his career in Houston.
"I don't know what all that entails," he said. "I've been traded a bunch of times in my career and it's no different. I chose Houston because it's close to home and I want to help this team win and I feel like I've been doing the best I can this year.
"Like I said all year, I'd like to stay here this year and obviously beyond that and finish my career as an Astro. It's not in my hands, though, so I don't really put too much thought into it."
FOX also reported Monday that Astros starter Scott Feldman cleared waivers, which means he could be traded to any club. He's in the first year of a three-year, $30 million deal that will play him $12 million this year, $10 million next year and $8 million in 2016.
Feldman, who's served a key role as the veteran to a young pitching staff this year, struck out five and allowed three runs in seven innings in Monday's 8-2 loss to the A's. Nine of his past 12 outings have been quality starts.
"I did see that, but when I'm pitching I don't really think about it," Feldman said. "Human nature, you wonder what's going to happen. When I'm playing, I'm just thinking about the guy that I'm facing. We'll see what happens."
Brian McTaggart is reporter for MLB.com and writes an MLBlog, Tag's Lines. Follow @brianmctaggart on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.