Anderson was primarily a starter for the A's in his first stint with the team from 2009 to 2013.
If added to the 40-man roster, he would get a $1.5 million salary while in the major leagues.
The 30-year-old had a 6.34 ERA and a 4-4 record in 13 starts last year for the Chicago Cubs and Toronto Blue Jays, who acquired him on Aug. 15. He signed a $3.5 million, one-year contract with the Cubs during the 2016 offseason.
Anderson has dealt with several injuries during eight big league seasons and was limited to six starts with Chicago because of a lower-back strain before being designated for assignment on July 26.
Anderson also was sidelined for much of the 2016 season because of surgery for a bulging disk in his back and a blister on his pitching hand.
He was 10-9 with a 3.69 ERA in a career-high 31 starts in 2015, helping the Los Angeles Dodgers win the third of four straight National League West titles.
Anderson is 42-47 with a 4.04 ERA in 128 starts and 12 relief appearances with Oakland, the Colorado Rockies (2014), the Dodgers (2015-16), the Cubs and Toronto.
The Associated Press contributed to this report.