A couple of things on this.
Chicago still owns his MLS rights, so anything would have to go through Chicago, either a loan there, or some form of trade where Chicago gets GAM (their favorite).
Talking with some Chicago fans, they think perhaps Gutman may be pissed at Chicago for what they offered him and didn't want to be loaned there (this was not a sale to Celtic, Gutman turned down the Chicago offer and signed with Celtic), so instead goes to Nashville for a year. He should have been able to get plenty of PT at Chicago since they no longer have any LBs after Brandon Vincent retired.