Putz will throw again Friday, according to a Cubs source.
Agent Craig Landis said Putz will be shut down after that until early January.
Putz also is seriously being considered by the Chicago White Sox.
Upwards of 12 teams will have looked at Putz, who ideally could be a primary set-up man or a closer if he's able to become 100 percent healthy again. Putz, who was one of the top relievers in the majors with the Seattle Mariners before being traded to the New York Mets last year, is recovering from surgery in his pitching elbow to remove bone chips.
Bruce Levine covers baseball for ESPNChicago.com.