Carrasco, who has been out since June 5, threw a bullpen session and did fielding work Tuesday.
Francona said Tuesday that he appreciated Carrasco's desire to push his comeback.
"The fact that he feels he's ready to do that is tremendous," Francona said. "Even if this just helps him feel better, that's OK with us."
Carrasco had to receive medical clearance before he was allowed to throw against batters.