Andrew Bailey threw scoreless innings on back-to-back days in Pawtucket on Wednesday and Thursday (AP)

PAWTUCKET — Red Sox reliever Andrew Bailey is close to making his return to the majors.

The right-hander achieved what he described as a “milestone” on Thursday, delivering a scoreless inning and striking out two (while allowing an opposite-field single) in the second of back-to-back games. He topped out at 94 mph while working mostly in the low-90s, got swings and misses on his fastball, cutter and curve and suggested that he feels nearly ready to pitch in the majors.

“I definitely accomplished the goal of going back-to-back. Just another step in the right direction. Able to execute pitches when need be. Good building block off yesterday,” said Bailey. “I feel real close. I’m just kind of going along with the process here. We’ll re-evaluate tomorrow and go from there. I definitely am feeling good and itching to get back. I’ve been itching since April 1. … It’s been a long season, and it’s not over yet. We’ve got some ballgames to win. I can’t wait to join the guys and get some W’s.”

Bailey said that he and the team have yet to discuss when he’ll be ready to return to the majors, waiting until he got through Thursday’s outing before considering the next step. Still, in five rehab appearances (two in the GCL, one in Double-A Portland and two in Triple-A Pawtucket), he’s sailed through five innings of work, allowing one run, striking out nine and walking one. Bailey said he was waiting to find out whether he would head to Cleveland on Friday to join the club or if he will remain in Boston for either evaluation or a new destination for his rehab assignment.

Bailey said that his cutter wasn’t quite as effective on Thursday as it had been on Wednesday, but he compensated with a fastball that he was better able to spot. He also proved able to bury his curve on a couple of occasions, using it as an out-pitch.

It remains to be seen where Bailey’s next stop will be, but soon, after a long wait that commenced when he required surgery on a torn ulnar collateral ligament in his right thumb just before the start of the season.

“I can’t wait to join the team,” said Bailey. “Hopefully, that’s soon. I can’t see it being too much longer.”