Astros general manager James Click said Sunday that Mushinski (elbow) could begin a rehab assignment at Triple-A Sugar Land during the upcoming week, Chandler Rome of the Houston Chronicle reports.

Mushinski has been on the 15-day injured list since June 7 with left elbow discomfort and will likely need at least two appearances in the minors before he's deemed ready to rejoin the big-league bullpen. Prior to being shelved with the injury, Mushinski covered 6.1 innings and gave up three earned runs on five hits and three walks while striking out eight across his six relief appearances for Houston.