Garoppolo (shoulder) is expected to take part in Tuesday's walkthrough practice, ESPN.com reports.
The Patriots still hope Garoppolo can start Thursday's game against the Texans, or at least get healthy enough to serve as Jacoby Brissett's backup. The team still hadn't signed another quarterback as of Tuesday morning, and any new addition wouldn't have a chance to practice before Thursday's game. Garoppolo was diagnosed with a sprained AC joint, an injury that quarterbacks are sometimes able to play with, though typically not with just three days rest.