The 29-year old Northern Ireland winger did not travel with the Hoops on their preseason tour of Germany with manager Neil Lennon suggesting a shift to St Andrew's could soon be completed.
"Paddy's gone and I think he's talking to Birmingham," said Lennon.
"I would recommend Paddy to anyone. He didn't play as much football as he would have liked at Celtic but he's a great pro.
"He was well respected in the dressing room and he was a valuable player to me over the past three years."