The Athletics reinstated Alexander (shoulder) from the 15-day injured list Wednesday.
Alexander (shoulder) came away from Monday's live batting practice session feeling healthy, MLB.com reports.
Alexander (shoulder) will face hitters Monday before a decision is made on whether he'll need a rehab assignment, MLB.com reports.
Alexander (shoulder) threw approximately 20 pitches in the bullpen before Friday's game against the Rangers and looked good, the Associated Press reports.
Alexander (shoulder) threw a bullpen session Saturday and could face live hitters at some point this week, the Associated Press reports.
The Athletics placed Alexander on the 15-day injured list Tuesday with left rotator cuff tendinitis, retroactive to Aug. 18.
Alexander (1-2) got the victory over the Diamondbacks on Friday, allowing an earned run on a hit and a walk over one inning.
Alexander (0-2) took the extra-inning loss against the Twins on Friday, allowing an unearned run on a hit and an intentional walk without recording an out.
Alexander (0-1) took the loss against the Padres on Tuesday, allowing an earned run on one hit and one walk over two-thirds of an inning.
Alexander was credited with his first hold in Saturday's win over the Astros, firing a scoreless two-thirds of an inning.