A source with knowledge of the situation indicated the Cubs would be interested in signing him if he is put on waivers.
Carpenter was the final compensation that the Red Sox received for allowing former general manager Theo Epstein to leave in order to become the Cubs' president of baseball operations.
Carpenter, who had elbow surgery in the summer of 2011, pitched for the Red Sox's Triple-A affiliate in Pawtucket and with the parent club briefly toward the end of the 2012 season. He appeared in eight games and had a 1-0 record with a 9.00 ERA, recording 10 walks and two strikeouts.
The Red Sox have 10 days to trade Carpenter before they must put him on waivers. If no club claims Carpenter, Boston could re-sign him to a minor league contract.
Like Boston, the Cubs also have a full 40-man roster, which would most likely preclude a trade between the clubs.
The Cubs would not comment on interest in Carpenter when contacted by ESPN Chicago.com.