Cespedes, who had procedures on his right heel on Aug. 2 and his left heel on Oct. 26, is hitting off a tee, playing catch and bicycling up to 40 miles, but he has not started running.
"He feels great every day -- a lot better, just normal activity, daily life than he did before because his heels were so painful," manager Mickey Callaway said.
Cespedes, 33, likely will return at some point in the second half of the season. He was limited to 38 games last year.
"When Cespedes gets back and we put this lineup together, it's going to be really, really special," Callaway said.
Meanwhile, Robinson Cano, who was hit on the outside of his left hand by a pitch on Sunday, was out of the starting lineup for the second straight day because of swelling.
Callaway said Cano felt better Tuesday. It was unclear whether he would be available as a pinch hitter against Cincinnati on Tuesday night.
The Associated Press contributed to this report.