"Nothing's been determined or really even discussed yet," Blevins said, "but at this point, where we are right now, it might be best not to push it."
The A's entered Saturday's contest against the visiting Rangers standing eight games back, with nine left on the schedule. Texas needs just one win and an Oakland loss this weekend to clinch the American League West title, a feat that would likely shelve Blevins.
"The competitive part of you wants to be out there, wants to finish the season healthy," he said. "But this isn't something I've dealt with before, so we're trying to be careful."
Blevins underwent "more extensive" drills with A's strength and conditioning coach Bob Alejo on Saturday morning, but he's yet to resume throwing. The southpaw compiled a career-high 48 2/3 innings a year after he tossed just 22 1/3 innings in 20 appearances through three stints with Oakland in 2009.
Blevins had not allowed a run in seven of his past nine outings before he succumbed to the shoulder injury following his most recent appearance, a one-inning relief stint in Kansas City on Sept. 15. His absence will leave Craig Breslow as the lone lefty in an injury-ridden bullpen, which also lost Andrew Bailey to season-ending elbow cleanup surgery this past week.