Barring any setbacks, the lefty is likely nearing a rehab assignment, which would put him just weeks away from a potential return to big league action.
The A's signed O'Flaherty to a two-year, $7 million deal in the offseason and initially didn't anticipate his return until July.
The lefty compiled a 1.45 ERA in 161 appearances over the previous three seasons, which is the lowest mark among Major League relievers with 125 or more innings pitched over that span.
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.