The lefty, signed by the A's to a two-year, $7 million deal in the offseason, is expected to utilize all of his pitches from a normal length in his next session.
"He looked really good," Melvin said. "You can see what he's got to offer, and it's pretty exciting. We'll take it on the pace we've been taking it on, but it was good to see him throw his breaking balls."
O'Flaherty appears to be ahead of schedule. Originally anticipated to be back in July, there's a chance he could join the A's as soon as June, given his current progress. By the time the A's return from their next road trip in early May, O'Flaherty is expected to be throwing to hitters.
"Then we start to get him out on a rehab assignment to where he's throwing in games," said Melvin. "That's when we can start to formulate a plan."
The 29-year-old southpaw was one of baseball's best relievers over the last three seasons, recording a 1.45 ERA in 161 appearances for Atlanta -- the lowest mark among any reliever with at least 125 innings.