BOSTON -- Free-agent reliever Scott Atchison, who was in the Red Sox's bullpen from 2010-12, threw his first full-fledged bullpen session of the winter on Monday, and this week he expects to announce what team he'll be pitching for in '13.

Barring something unexpected, that team will not be the Red Sox, Atchison told MLB.com on Monday. Atchison is looking at a Minor League deal, and he'll choose a team he believes gives him a very good chance to make the big league club.

"We're pretty close. We're not completely final yet, but I pretty much have a deal," said the right-handed Atchison, who turns 37 in March and spent the last three seasons with the Red Sox. "I prefer not to say who right now because it's nothing final, but we're not really out there any more, I guess for the most part, unless something fell apart here in the next day, which I don't foresee. It took a little longer, though, than I guess I expected. Some teams were pretty cautious with the elbow. I think some of that was more to do with my age than anything, age and the elbow. It's kind of like, 'OK, well, you're 36, going to be 37, and you do have this tear.' Everybody knows about it, obviously."

The throwing-elbow situation is a partial tear of Atchison's UCL that he was advised in August could heal with rest and rehab, and he said the results have been great. He's been working out at home in Texas and started throwing full-bore in December.

"Other teams were kind of like, 'We're not that worried about it. He was throwing at the end of the year, everything looked fine and that's not really that big a deal, honestly,'" Atchison said. "It's more a situation that the team's in. ... Had no problems, everything feels normal, so I haven't had any issues. Obviously it is what is with the tear and stuff, but nothing that's restricting me. At the end of year, I felt great. I feel normal, and with another couple months of rest, it seemed to hopefully calm it down even more."

Atchison's time with the Sox followed a two-year stint in Japan with the Hanshin Tigers. He went 5-4 with a 3.18 ERA in 102 games and 141 2/3 innings, with 94 strikeouts and just 34 walks during his time in Boston. Next season will be Atchison's seventh in the Majors.

From 2010-12, Atchison had the sixth-best walks-per-nine-inning rate among American League relievers with at least 100 innings pitched: 2.14. That's ahead of Joe Nathan and Jonathan Papelbon.

Still, it's been an uphill climb for Atchison this offseason, just as it's been his whole career.

"I guess the offseason has kind of mimicked maybe my career a little bit," Atchison said. "'All right, give me a chance.' And somebody's excited and maybe they get turned off by something."

Atchison would have liked to come back to Boston. Doctors and physical therapists here have been great for his 5-year-old daughter, Callie, who has a rare genetic disorder. Callie is doing very well, and this month marked three years since her last surgery.

Atchison called his time in Boston great, and while the Sox did make an offer after he was non-tendered, he wanted a situation with a better opportunity.

"I think we were really hoping that Boston would go ahead and tender me in a contract at the time back in December, and the thing didn't work out and that's not where we're going to end up this year," Atchison said. "We definitely enjoyed our time there and the experience and the uniqueness of all of it."

"Kinda quiet," Atchison said of Boston's approach with him. "They offered a Minor League deal, and just really that was pretty early on, right after. As their situation changed with bringing in more right-handed arms, I really didn't feel like it was going to be much of a fit. I was going to be forced to probably have to start the year back in [Triple-A] Pawtucket. And I felt that wasn't really what I had deserved and what I had earned with them in that situation. I felt like if I'm going to start somewhere in Triple-A, I want to start somewhere new, I guess, if that was the case."

Now it seems certain Atchison is on to greener pastures.

"It's not going to be a Major League deal, but it's going to be a situation where I'm going to have a pretty good chance to make a team; there's some openings in their 'pen," Atchison said. "It's been a fun three years, and you know, who knows? You never know, I could always end back up there somehow. It's probably not going to be at the start of this year."