Manager Kevin Cash said he expects an update after the Rays' three-game series in Boston. Tampa Bay opens a four-game series at home against the Texas Rangers on Thursday night.
Cobb hasn't pitched this season, and his rehabilitation program has been shut down. The Tampa Bay Times reported Tuesday that he has a partial ligament tear in his elbow.
The newspaper also said Cobb will try to pitch through it after receiving platelet-rich plasma therapy. If that is unsuccessful, he would need Tommy John surgery, according to the report.
In four seasons with the Rays, the 27-year-old Cobb is 35-23 with a 3.21 ERA. He was 11-3 with a 2.76 ERA in 2013 and 10-9 with a 2.87 ERA last year.