Doherty, the front man for Babyshambles, is famous for his battles with drug addiction and his brushes with the law.
The Daily Mail said Sting was furious when he heard Doherty had been resting in Coco's tent after his performance at England's recent Glastonbury music festival.
"I was standing next to Coco's tent after Pete had played his set and one of her friends went to check on her," an onlooker told the newspaper. "She unzipped the door and Pete was lying outstretched in her tent. He looked very comfortable and was smoking something -- the tent was full of smoke but it was impossible to tell what it was. He seemed pretty out of it, though. Coco's father isn't too happy about her hanging around Pete because of his reputation and hit the roof when he heard he had stayed in her tent."
Sumner, an aspiring singer, songwriter and guitarist, met Doherty at a jazz bar in London in March, and Doherty has since been helping her with her upcoming debut album.
"Pete has been raving about her talent. It's pretty clear he has the hots for her too, which will only worry her dad more," the source told The Daily Mail.