Cobb has not pitched this season after leaving a spring training start on March 17 with tendonitis in his forearm.
Cobb experienced a setback in his recovery, putting his 2015 season in jeopardy.
According to the report, Cobb is expected to attempt to resume pitching in about two weeks after seeing if the platelet-rich plasma therapy he received is working.
If his ligament is not healed, Cobb could be looking at Tommy John surgery, which would sideline him for the next year to 18 months.
"We're continuing to do the evaluation to figure out what the next steps are," general manager and President of Baseball Operations Matthew Silverman said. "At this point, Alex is focused on getting back on the mound and pitching this season for the Rays, but there is no timetable yet."
Silverman said there is no timetable for Cobb’s return and the team will continue to monitor his progress.
"We have followed and continue to follow normal protocol with this type of injury," Silverman said. "It was a forearm strain. The forearm is closely connected to the elbow, so there is always concern with a forearm strain."
Cobb is making $4 million in 2015 in his first season of arbitration eligibility and is under the team's control for the next three seasons.
He had a 10-9 record with a 2.87 ERA and 149 strikeouts in 166 1/3 innings last season for Tampa Bay.
- Scooby Axson