Britton told ESPN that he injured himself running sprints Tuesday. He said he's hoping to return a "little quicker'' than the six months projected for his Achilles rehab.
"Since I'm a pitcher and don't have to run bases, I could be back before that,'' he said. "We will know more after surgery tomorrow.''
The left-hander had been the subject of trade rumors because he will be a free agent at the end of the 2019 season. He was set to earn more than $12 million in arbitration.
Britton, 29, was the most dominant reliever in baseball in 2016. He led the league with 47 saves and had a 0.54 ERA and 0.836 WHIP. He was an All-Star and finished fourth in Cy Young voting.
But injuries slowed him last year. An MCL strain in his left knee required platelet-rich-plasma treatment.
He was limited to 38 games and had a 2.89 ERA, 1.527 WHIP and 15 saves.