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7/6/2014 8:37 P.M. ET

Yankees designate Soriano for assignment

MINNEAPOLIS -- After making a trade to bolster their rotation, the Yankees let go of a familiar name.

New York designated outfielder Alfonso Soriano for assignment on Sunday after acquiring starter Brandon McCarthy from the D-backs for pitcher Vidal Nuno. The Soriano move allowed New York to bolster its bullpen by calling up right-hander Bruce Billings from Triple-A Scranton/Wilkes-Barre.

"It's extremely difficult, because he's been a great Yankee and a great player," manager Joe Girardi said.

Soriano was batting .221 over 67 games this season, and he hadn't been able to display the power he showed after the Yankees traded for him last June, hitting only six home runs. He totaled 17 homers and 50 RBIs over 58 games with New York in 2013.

When pitching depth became a concern, Soriano was the odd man out in an outfield that already included veterans Ichiro Suzuki and Carlos Beltran.

"He never made excuses," Girardi said. "Never. I knew his wishes. I knew he wanted to play every day in the outfield. But that was Ich. That was Carlos, too. It was kind of difficult."

The 38-year-old spent parts of seven seasons at the big league level with New York, and he was named to seven straight All-Star Games from 2002-08 with the Yankees, Rangers, Nationals and Cubs.

Teammate Derek Jeter was especially sorry to see Soriano go.

"Soriano's like family to me," Jeter said. "Played together with him for a long time. When he first came up, and then obviously, coming back now. So Sori's had a tremendous career here in New York. He's done a great job. It's difficult for him this year. Any time you talk about a player that's used to playing every day not playing every day, it's kind of hard to be productive.

"I feel for him. I'm going to miss him, but I will be in touch with him because he's like a brother for me, and he should be proud of what he's been able to do -- not only in the past but this year as well. I wish him nothing but the best."

Billings was 4-4 with a 5.31 ERA in 11 starts at Triple-A this year. He allowed four runs in four innings vs. the Angels on April 25 in his lone appearance for the Yankees this season.

The 28-year-old is expected to be available in a relief role for the short term, but Girardi said Billings will not be filling the rotation hole on Monday.

"We felt we needed more pitching today," Girardi said. "If something happened to Hiroki Kuroda early today, we'd be in a pickle, so we called up Billings. Our bullpen has been extremely taxed.

"For Sori, it's a guy who came in and did a tremendous job for us last year. He's had his struggles this year, and he's a guy who's used to playing every day. It wasn't everyday at-bats for him, so maybe it was harder for him to get going."

Greene to be summoned to assume Nuno's start

MINNEAPOLIS -- It's official: Brandon McCarthy will be taking the mound for the Yankees on Wednesday. But more immediately, Shane Greene will be called up from Triple-A Scranton/Wilkes Barre to start Monday's game vs. the Indians.

Manager Joe Girardi announced the new rotation order after Sunday's 9-7 win against the Twins.

Vidal Nuno, the departing piece of Sunday's deal for McCarthy, was penciled in to start on Monday night in Cleveland, and it initially appeared as if callup Bruce Billings would take his place.

But before Sunday's game, Girardi said that Billings will not start on Monday, and that the eventual starter might not be on the current 25-man roster.

"It's possible," Girardi said.

After the game, the manager announced that Greene will start. The right-hander has gone 5-2 with a 4.61 ERA in 13 Triple-A starts this year.

Does Girardi envision Greene sticking around for more than one Major League appearance?

"Every opportunity is an opportunity to shine and get more opportunities," Girardi said.

Barring injury, McCarthy will get plenty of chances to stick. He brings a 3-10 record and 5.01 ERA to the Yankees, but has been much more solid in his two most recent starts (2-0, 2.13 ERA). Can he keep it up?

"He's got too good of stuff not to," Girardi said.

Worth noting

• After taking batting practice Sunday morning, Brian McCann (sore right foot) was back in the Yankees' lineup vs. the Twins and ripped an RBI double in his first at-bat.

Girardi said McCann's MRI results came back "very good," paving the way for the catcher's return.

Alex M. Smith is an associate reporter for MLB.com. Follow him on Twitter @asmiff. This story was not subject to the approval of Major League Baseball or its clubs.