Bazardo has three business days to decide to accept the assignment or reject it and become a free agent.
"We'd like him to stay in the organization," Astros general manager Ed Wade said. "We like his arm. Unfortunately, he couldn't get things going in Spring Training, and now that he's healthy again, we think he has a chance to help us at some point."
Bazardo, signed as a Minor League free agent last April, put up terrific numbers at Round Rock last year, going 9-6 with a 3.20 ERA in 23 games, including 20 starts. He was named a Pacific Coast League All-Star and was Round Rock's Pitcher of the Month in May.
The 25-year-old had his contract purchased Aug. 8 of last year, and couldn't duplicate his success with the Astros, going 1-3 with a 7.88 ERA, allowing 37 hits and 22 walks while striking out 17 in 32 innings. He strained his shoulder early in Spring Training and had been on a rehab assignment.