Alvarado (personal) threw a bullpen session Thursday, and the Rays hope he'll need only a few more side sessions and possibly a simulated game before returning to the team, Eduardo A. Encina of the Tampa Bay Times reports.
Alvarado is currently on the restricted list after leaving the team to be with family Venezuela at the beginning of June, and he'll have to go through an abbreviated spring training prior to being activated. However, the Rays are optimistic that he'll be able to avoid a minor-league stint, which will likely speed up the process. There's currently no timetable for Alvarado's return.