A core special-teams player, Cole has 15 tackles and an interception for the Patriots this season.
No corresponding roster move has been made at this time.
The team previously waived Cole earlier this year and promoted practice squad safety Kanorris Davis to help fill Cole's special-teams duties. The move was tied to an injury to Cole, who was re-signed shortly thereafter.
It's unclear whether he has suffered another injury, perhaps during practice Thursday. Cole was not listed on Wednesday's injury report, but he has been hampered lately by a calf issue.