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5/25/2014 2:30 P.M. ET

Pineda making progress, feels good after throwing BP

CHICAGO -- Michael Pineda is making progress as he aims to rejoin the Yankees' starting rotation in June.

The right-hander had no issues a day after tossing 28 pitches of live batting practice and has been scheduled to throw two innings in an extended spring game on Tuesday at the club's complex in Tampa, Fla.

Pineda has not pitched in a big league game since April 23, the day he was ejected from a start against the Red Sox at Fenway Park for having a large smudge of pine tar on his neck.

He accepted Major League Baseball's 10-game suspension for the incident, then strained a muscle in his upper back while throwing a simulated game in an attempt to stay sharp.

Yankees manager Joe Girardi said that he believes Pineda would probably throw in one more extended spring game if Tuesday's outing goes well, bumping up to three innings, and then could be cleared for Minor League rehab starts.

"I think when you start to see him throwing three and four innings, and bouncing back, you know that he's getting fairly close," Girardi said.

Pineda had a 1.83 ERA in four April starts before the suspension and the injury. Girardi said that the Yankees are eager to get him back, but they would want Pineda to build up to throw 75 to 85 pitches before he would be added to the active big league roster.

"As long as he has no setbacks, he'll be coming pretty quickly here," Girardi said.

Pineda missed all of the 2012 and '13 seasons following right labrum surgery. Because of that, the Yankees thought they might have to scale back his outings later in the season, but Pineda's stint on the disabled list has erased that concern, assuming that he can come back healthy.

"We never set a limit on innings," Girardi said. "It was more of how he's doing physically and watching his stuff, but he's missed a substantial period of time here. You would think that he'd probably be able to go out most of the year."

Girardi expects confident attitude from Tanaka

CHICAGO -- Masahiro Tanaka broke out laughing, even before his interpreter could parse his response from Japanese into English. The Yankees' pitcher had been asked if he would fix a problem from his last start, working up in the strike zone too much.

"Just watch me in the game," Tanaka said.

As Tanaka takes the mound on Sunday for his 10th big league start, Yankees manager Joe Girardi said that he has come to expect a confident attitude from the 25-year-old right-hander, for whom no challenge seems to be too great.

"The adjustments he's made in games, the adjustments he's made to the five-man rotation, the culture -- everything that he's done so far to this point would make you believe that he doesn't make too much of one game," Girardi said.

"There's been a lot of games that he hasn't been happy with at one point in the game and he's pitched pretty well. He has high expectations."

One of Tanaka's biggest adjustments in coming from Japan to the Majors was expected to be his transition from pitching once a week to operating in a rotation that would give him the ball once every five days. Tanaka described that adjustment as "pretty normal, not at the best, not at the worst."

Girardi said that the Yankees remain cognizant of Tanaka's adjustment when they consider his pitch counts, but they do not feel the need to check in about his stamina before and after every start.

"I'm going to watch his stuff more than anything," Girardi said. "That's going to tell me where he's really at, opposed to what he's probably going to tell me.

"To be who he's been and what he's done so far in his career, you're always going to want to be out there. It'd be like asking [Derek Jeter] how he is."

Bombers bits

Carlos Beltran (bone spur in right elbow) continues to be scheduled to take dry swings on Monday in New York. The results of that session, which will be watched by assistant athletic trainer Mark Littlefield, could determine if Beltran can play through his injury. If he requires surgery, Beltran would miss 8-12 weeks.

"It might take a few days, but you might know right away," Girardi said. "Obviously, dry swings are different than making contact, and making contact is different than swinging and missing at full speed."

Shawn Kelley (lower back strain) is scheduled to play catch on Monday and could rejoin the team in June. ... Francisco Cervelli (strained right hamstring) has been running bases and is on track to be activated from the 60-day disabled list when eligible in June.

• Sunday's contest against the White Sox concludes the Yankees' unusual six-game, two-stadium, one-hotel trip to Chicago, having played two games at Wrigley Field on the same visit.

"It's been good. The guys have enjoyed not having to pack up and get on planes. It's been nice," Girardi said.

• On this date in 1998, Hideki Irabu threw a shutout in the Yankees' 12-0 win over the White Sox in Chicago, improving to 4-0 and lowering his ERA to 1.13.

Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.