MINNEAPOLIS -- It shouldn't be too long before Eddie Rosario's big bat is back in the heart of the Twins' lineup.

Rosario did some straight-line running at Target Field before Friday's series opener against the Rangers, and manager Rocco Baldelli characterized the session as another positive development in the outfielder's quick recovery. Rosario, who sprained his left ankle while running the bases on June 26, is eligible to be reinstated from the 10-day injured list on Sunday, but the Twins will likely keep him out of action until after the All-Star break.

"I would say it’s unlikely that we are going to activate him before the break, but once the break ends, we’re hopeful that he’s going to be ready soon," Baldelli said.

Unfortunately for the Twins, the multi-positional Willians Astudillo's recovery is coming along more slowly. Astudillo has been on the injured list with a left oblique strain since June 27 and he won't progress to baseball activity for "a little while," according to Baldelli. The skipper did not offer a more specific timeline, but he made it clear that Astudillo's return would not be imminent following the All-Star break.

Astudillo said he initially hurt the oblique when he ran into a wall while making a leaping catch in foul territory on June 25, and he felt pain on a swing the following day.

"There’s not a lot that he can do in the early parts of his rehab," Baldelli said. "An oblique-related injury is not something that just heals up and all of a sudden you start taking swings and throwing. It’s a fairly significant oblique injury, and so we are going to have to let him heal before we can do anything."

Parker to paternity list; Stewart recalled

The Twins placed reliever Blake Parker on the paternity list on Friday and recalled Kohl Stewart from Triple-A Rochester in a corresponding move.

Stewart, who started for the Red Wings this past Sunday, could be a candidate to make the start in the final game of the first half this Sunday in place of the injured Jake Odorizzi. The Twins could also turn to left-hander Adalberto Mejía, who was reinstated from the 60-day injured list on Tuesday, though their starting plans will likely be dictated by whether Stewart or Mejia is needed out of the bullpen in the coming days.

The 24-year-old Stewart has a 4.50 ERA with four strikeouts and five walks across 16 innings in a pair of spot starts and an extended relief appearance for the Twins this season.

"Kohl is here to help stabilize everything going on," Baldelli said. "He could help fill a few different roles. We don’t know how he’s going to be used yet to this point, but he’s done a nice job for us with basically everything we’ve asked him to do to this point, so it’s a good feeling, being able to call him up."

Buxton feeling more pressure

Because Byron Buxton has a strong comfort level playing in outfields alongside Max Kepler and Rosario throughout the Minor Leagues and in the Major Leagues, he has had to adjust mentally during this recent stretch in which the Twins' outfield depth has been tested by numerous injuries that have forced infielders Luis Arraez, Ehire Adrianza and Astudillo into the corner outfield spots at various times.

"It's easy for [Kepler, Rosario and myself] to just go out there and know, 'Oh, with where that ball's hit, that's [my] ball,'" Buxton said. "It's different when you've got somebody else out there. At the same time, it's teaching me, and I'm learning what I can and can't do, what I'm doing too much."

Because Arraez, a career infielder, has seen regular action in left field with Rosario on the injured list and Marwin Gonzalez having been dinged up over the last several games, Buxton said he has had to focus more on communication to help Arraez's comfort level with decision-making. Buxton has also had to learn to not try to do too much in an effort to overcompensate for the lack of natural outfield experience alongside him.

For example, Buxton pointed to Chris Herrmann's third-inning double in the Twins' 7-2 loss to the A's on Thursday, in which Buxton had been too aggressive on a line drive into the left-center-field gap in an effort to cut the ball off so that Arraez wouldn't need to handle it. Instead, the ball took an in-between hop on Buxton and bounced over his head to give Herrmann an extra base.

"I think I over-panic sometimes to try to do something so they don't have to do it, rather than just letting them go out there and be themselves," Buxton said. "I try to take some of that pressure off."