For now, Bradshaw is undecided about whether to have surgery, the source said.
Bradshaw, who has 186 yards on 41 carries this season, is unlikely to play Sunday against the Seattle Seahawks.
Bradshaw originally injured his neck in a Sept. 22 game at San Francisco. He did not practice last week and missed last Sunday's 37-3 victory over Jacksonville.
ESPN.com Colts reporter Mike Wells contributed to this report.