The deal is worth $8 million guaranteed and could be worth as much as $13 million if he pitches a full season, according to the reports.
Kluber, who turns 36 in April, was limited to 80 innings last season with the New York Yankees because of a shoulder strain that kept him out for more than three months. He went 5-3 with a 3.83 ERA in 16 starts for the Yankees and pitched a no-hitter in May, striking out nine batters in a 2-0 victory over the Texas Rangers.
The two-time Cy Young Award winner hasn't pitched a full season since 2018. He spent his first nine seasons with Cleveland and was a three-time All-Star, winning 98 games with the franchise and striking out more than 200 batters five times.
For his career, Kluber is 103-61 with a 3.19 ERA in 1,422⅔ innings over 11 seasons for Cleveland, Texas and the Yankees.