The competition to become the Houston Astros' closer will likely extend beyond spring training.
"I think that we will go into the season with a closer-by-committee and try to look at the best situation given that night, given that game," manager Bo Porter said Sunday.
Qualls appeared to be the favorite entering Grapefruit League games.
"I think all of those guys have done a really good job," Porter said. "When you don't have one guy that has separated himself, you would rather it be the way it is where all those guys are throwing the ball well, which is a good problem to have."
Should the competition continue into May, Jesse Crain could also become a contender. The Astros signed Crain as a free agent over the winter, but he is still rehabbing from offseason biceps surgery.
The Associated Press contributed to this report.