The team also plans to offer restricted free-agent tenders to eight players, the Tennessean reported Saturday.
"The Titans have not closed the door on Jason Babin at all," Rosa said. "We are in very uncertain waters right now with regard to the collective bargaining agreement, and once those issues are cleared up, we are going to address it. That's what the Titans told me. ... We don't know the rules we are going to be playing under."
"Sure, he would have liked an extension by now," Rosa said. "But it didn't happen, and we have to be patient and wait for things to get hashed out, and then we will address it. I have to trust their word on that."
The other players the newspaper identified were guard Leroy Harris; defensive end Jacob Ford; linebackers Colin Allred, Patrick Bailey and Tim Shaw, and offensive lineman Mike Otto. It is unclear if the tags will be binding once a new CBA is in place.
The Associated Press contributed to this report.