Osuna is in "fair" shape, manager Dusty Baker said. But he's on an accelerated plan to get into game shape.
While in Mexico over the past few months, Osuna was mostly isolated and unable to train the way he wanted.
Baker and pitching coach Brent Strom spoke about Osuna on Friday, and Strom assured the skipper that their closer would be ready when the season begins at the end of the month.
"He's on an accelerated course, but you've got to be careful because you don't want them to get hurt while they're accelerating themselves to try and catch up," Baker said. "Each individual is different, so we've got a close eye on him every day."
The Astros are quickly ramping up for the 2020 season, with just two weeks left before their July 24 opener against the Seattle Mariners.
Osuna is widely considered one of the best closers in the game. In his first full season with the Astros last year, he posted 38 saves with a 2.63 ERA. He and Ryan Pressly, who threw a live batting practice Friday at Minute Maid Park, arguably comprise the best late-inning pairing in Major League Baseball.