Galen's book might not be sought out by readers today, but the extensive annotations in Latin and Greek, especially in the chapters on human nature and on the bones ("Galeni de ossibus ad tirones liber"), show that early readers studied the book carefully. It is natural to assume that the author of the annotations was also  the owner of the book. Analyzing handwritten notes and comments can gives us some clues to the owner's identity.

Among the annotations in Volume II, there is a reference to Francisco Valle's commentaries on fevers published in 1592. The use of Emperor Rudolph's portrait on the binding suggests the owner might be someone from his circle who was still active when Valle's work was published. Once you eliminate those around Rudolph who could not author the annotations, the circle of potential second-in-line owners with medical backgrounds gets smaller.
The association with the Hapsburgs' court might be a wild guess, but imagining a naturalist or physician from the turn of the 17th century as a reader is quite plausible.