NEW YORK -- Red Sox reliever Tyler Thornburg is likely to join the club this week, manager Alex Cora said Sunday.

Thornburg pitched a 1-2-3 inning for Triple-A Pawtucket last night, needing only eight pitches. His rehab from thoracic outlet syndrome surgery has been up and down, though it appears he's close to making his season debut in the majors.

"He was good," Cora said. "He's around, and we were just talking about it. It'll either be one more [rehab] inning or he'll be ready for this week. We'll talk about it after the game and go from there."

If Thornburg is activated, the Red Sox will likely send righty Justin Haley back to Triple-A. Thornburg will join Matt Barnes, Joe Kelly and Craig Kimbrel at the back end of the bullpen, potentially giving the Red Sox the opportunity to not make a bullpen trade at the non-waiver trade deadline.

"I'm ready to get in an actual routine," Thornburg said Sunday. "It's tough when you spend so much time working toward something and kind of getting that taken away from you. It's incredibly tough, as well as being around these guys everyday and knowing there's not much I can do to help the team on a weekly or monthly basis. It's tough, so hopefully I can come in, make a huge contribution and make it all worth it."

Thornburg, who will turn 30 in September, was acquired at the 2016 winter meetings in a trade that sent Travis Shaw and two minor-leaguers to Milwaukee. While Shaw has been a consistent producer for the Brewers, Thornburg is yet to make an impact for Boston.