Coleman quit as Wales boss to take charge of the crisis-hit Black Cats, who are sitting bottom of the Championship.
Speaking on talkSPORT, Barton said: "They have just set the record for most home defeats, they are bottom of the table, there is a disconnect with the owner. I didn't see him taking that job.
"I thought he was better than that.
"He must be getting weighed in to go there and been given guarantees to spend in January.
"Has anybody seen if he is alright? Has anybody checked to see he is all there, if he has had any problems with his mind or lost his senses?