Alex Kirilloff took batting practice Sunday ahead of the Twins' 7-6 loss to Oakland at Target Field.

The rookie progressed from swings in Chicago last week, hitting off a tee and soft toss as he works to recover from a right wrist sprain. The injury, which Kirilloff declined to specify, has sidelined him on the 10-day injury list since May 4 and required a visit to a hand specialist.

But the rehab isn't quite straightforward.

"I'm just encouraged right now with how it's felt so far. Apparently, it's something that has been able to be managed before, and it's basically just what kind of symptoms that you're having," the first baseman/outfielder said. "It doesn't sound to me like something that you can make worse with using it and trying to go for it in terms of overall health and wrist health. So I feel comfortable just trying to push it as long as I don't have any heavy symptoms while doing it."

In addition to some of the swing work, Kirilloff has also been able to run, lift, throw and practice some outfield and fielding skills. He planned to take batting practice on the field Monday before ramping up to higher-velocity and off-speed pitches. In the next week or so, Kirilloff said he should know what his next step is.

The hope is he can return on a rehab assignment feeling close to 100% before eventually rejoining the team.

"I wouldn't really want to go out there if I felt like I couldn't be effective, and I think that's just part of being a professional and something that comes along with that," Kirilloff said, adding he had another right wrist injury, albeit it in a different area, in 2019 and played through that. "I wouldn't want to put my teammates or my team in jeopardy just because I wanted to go out and play to play. I wouldn't get out there unless I felt like I could be effective playing."

Surgery, though, is potentially in the future. It could be as soon as the next couple weeks, depending on Kirilloff's comfort in playing through any soreness or stiffness. Kirilloff said the doctors won't know the recovery time for that until they go in and see it. But it could be anywhere from weeks to months.

"If I can play and manage it now, great. But if I'm still feeling it a little bit, I'm probably going to get it surgically taken care of maybe at the beginning of an offseason," Kirilloff said. " … Or even a better scenario, there have been scenarios before where people just leave it alone because they just don't feel a need. It just depends. Time will tell."