NASHVILLE — With the A’s trade on the final night of the winter meetings, the team’s 2016 infield comes into focus and the most high-profile return player in the Josh Donaldson deal is gone.

Oakland sent infielder Brett Lawrie, acquired from Toronto a year ago, to the White Sox on Wednesday, a deal first reported by The Chronicle, and in return, the A’s received two minor-leaguers, right-handed reliever J.B. Wendelken and left-hander Zack Erwin. General manager David Forst said that Wendelken might contribute this season.

Forst said that the team doesn’t view the Lawrie trade to Chicago as any sort of statement about the Donaldson deal, though, especially with starters Kendall Graveman and Sean Nolin on the A’s staff and highly regarded minor-league shortstop Franklin Barreto in the system.

“We don’t look at it that way,” Forst said of tying Wednesday’s transaction to the Donaldson trade. “Obviously, trading (Lawrie) for two young pitchers extends the life of that trade. … We don’t look back a year and sort of connect the two, other than to say we continue to feed the system with this deal.”

Lawrie, 25, hit 16 homers and drove in 60 runs for Oakland, but drew comparisons with eventual league MVP Donaldson after the deal and was seen as something of a disappointment. “I never got the sense he felt he was trying to live up to anything,” Forst said of Lawrie. “He doesn’t lack for confidence. He played well and he worked really hard to keep himself on the field. He deserves a lot of credit for that; it was the biggest knock on him coming into the season, and it wasn’t an issue.”

When the A’s reacquired Jed Lowrie last month, it was obvious Lawrie would be the odd man out. His go-go-go style and off-the-charts intensity also grated some when the A’s found themselves in last place, but his ability is unquestioned. Many scouts believe he could be an All-Star, especially given his age.

Forst said that as things stand now, Danny Valencia will play third, Marcus Semien shortstop and Lowrie second base, with Eric Sogard in the utility spot.

Forst said that Wendelken took a big leap last year after moving into the bullpen; he has a nasty changeup and a fastball in the low 90s. Erwin, who pitched at Clemson, was a potential draft target for the A’s. Forst said they see him as joining a strong bunch of starters from last year’s draft who will come up together.

The A’s also finalized a two-year, $10 million agreement with reliever John Axford, who is expected to be the second setup man behind Ryan Madson, who agreed to a three-year, $22 million deal earlier in the week. Neither deal will be announced until Thursday at the earliest, because that’s when both will take their physicals. That’s handy timing, because Oakland’s 40-man roster stands at 38. The A’s have the sixth pick in the Rule-5 draft Thursday morning, and they’re likely to take a player — so they have to have an open roster spot.

However: They’re likely to turn around and send that player to San Diego to complete the Drew Pomeranz-Yonder Alonso deal of last week.

There is some chance that they’d then take another player with their second pick, and the second open roster spot at least gives them that option, but with two relievers to add this week, it’s hard to see where they’d stash a Rule-5 player. And it would be tough to carry a Rule-5 player on the 25-man roster the entire season when they already have two roster spots that are somewhat problematic: Outfielder Coco Crisp, due a team-high $11 million in 2016, has not been available consistently for more than a year because of a chronic neck issue, and designated hitter Billy Butler, who is owed $20 million over the next two years, underperformed in 2015, with a .251 average, 20 points below his previous career low.

Crisp, one of the team’s best players when healthy, is untradeable because of his neck condition. Butler is virtually untradeable because of his contract, his lack of production and his lack of versatility.

“You can’t trade him to an NL team; he’s totally one-dimensional and when he’s not hitting, he can’t do anything,” one major-league executive said. “I don’t see any of the other AL teams looking for a DH with a bad body coming off two down years. ... They’re just going to have to hope he turns it around, but I’ll never understand that contract they gave him.”

Susan Slusser is a San Francisco Chronicle staff writer. E-mail: sslusser@sfchronicle.com Twitter: @susanslusser