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3/3/2013 7:16 P.M. ET

Gallardo feeling better, but Classic status murky

MESA, Ariz. -- Brewers ace Yovani Gallardo was back on track for the World Baseball Classic after testing his strained right groin in a successful bullpen session on Sunday morning. Whether he pitches for Team Mexico will be decided Tuesday, when Gallardo is scheduled to pitch an inning in a game.

The question is, which uniform he will don for that outing?

The Brewers would prefer he start Milwaukee's exhibition against Canada's Classic entry at Maryvale Baseball Park on Tuesday afternoon. But to do so, Gallardo would have to skip Mexico's team meeting on Sunday night and a workout on Monday.

"The rules are that if he shows up to the meeting that they have, he cannot come back with us," Milwaukee manager Ron Roenicke said. "He cannot come back to get treated, he can't come back to pitch an inning on Tuesday for us. So I need to have a discussion with 'Yo' to see what he wants to do. They have a game on Tuesday night [an exhibition against the D-backs], so if he would rather pitch that inning for them, then we'll do that.

"His bullpen [session] was good today. We would rather have him with us, but I get that he would want to be with them because he is going to miss out on some stuff, some fundamentals that they do [on Monday]. I get it."

Because Gallardo's strain is minor, Brewers medical officials are relying on input from the pitcher himself to make a final determination about the Classic. Gallardo badly wants to represent Mexico this time after withdrawing from the 2009 event because he was returning from knee surgery, but has promised Roenicke he'll be smart.

"He'll do the right thing," Roenicke said. "He'll tell us if something is going on."

Gallardo pitched two scoreless innings against the Mariners on Tuesday before allowing three runs on a pair of homers in the third. He said he first felt some discomfort between the first and second innings and was sore that night and the next day, but has steadily improved since then. By Sunday, Gallardo was feeling "a lot better" after several days of playing catch with no setbacks.

He was not available to reporters after his mound session, but was asked beforehand for a gut feeling: Is he healthy enough to pitch for Team Mexico?

"Yeah, I am. I mean, I think I am," Gallardo said. "Unless there's something crazy that happens today where it goes back to how it was after that game [against the Mariners]."

Before his groin became an issue, Gallardo was lined up to pitch Mexico's second game in the Classic, against Ryan Braun and Team USA on Friday night at Chase Field. The backup option is another Brewers right-hander, Marco Estrada, who allowed only one Cubs hit in four scoreless innings on Sunday.

"If there is [discomfort], it's something you have to think about a lot more," Gallardo said. "Going into the WBC, you want to feel 100 percent. I have to make sure it's right, and I know my body well enough to know how it's going to react to certain things."

Adam McCalvy is a reporter for MLB.com. Read his blog, Brew Beat, and follow him on Twitter at @AdamMcCalvy. This story was not subject to the approval of Major League Baseball or its clubs.