While not addressing any players specifically, Luhnow hinted the Astros could make a deal soon.
"We're optimistic that there are going to be some improvements to the club we can make within the next week," he said Wednesday from his suite at the Opryland Hotel.
Giles, 25, had a 1.80 ERA and 15 saves in 17 opportunities as the Phillies' closer last season. The righty, who won't be a free agent until after the 2020 season, averaged 96.5 mph with his fastball and struck out 87 batters in 70 innings in 2015.
Luke Gregerson posted a 3.