Boxberger finalized a one-year, $2.8 million contract with Chicago in December, but he had trouble staying healthy for much of the season.
The 35-year-old Boxberger was placed on the 15-day IL on May 15 with a right forearm strain. He was activated Sept. 8 and got into five games this month before landing on the IL again.
The right-hander is 0-1 with two saves and a 4.95 ERA in 22 games on the year. He had a 3.34 ERA in 71 appearances with Milwaukee in 2021 and went 4-3 with a 2.95 ERA in 70 games with the Brewers last year.
Chicago has been hit hard by injuries as it fights for a National League wild-card down the stretch.
Closer Adbert Alzolay, who is on the injured list with a right forearm strain, had a bullpen session Friday that went well. He was slated to play catch Saturday.