Cotts, 35, signed a one-year, $3 million contract with Milwaukee in January. He's 1-0 with a 3.28 ERA in 50 games this season. He's 21-24 over 10 seasons, including stints with the White Sox, Cubs and Rangers.
Cott had Tommy John surgery in July 2009, did not pitch in 2010 and '11 because of arm and hip injuries, then spent 2012 in the Rangers' minor league system. He made his debut for Texas on May 31, 2013, his first big league appearance since May 25, 2009.
The Associated Press contributed to this report.