He is of skinny build and about 180cm tall. He appeared to have dark hair and was wearing grey clothing.
Doyle said he thought his personal items would be safe in the changing rooms.
"I would really like my property back and next time I will be keeping an eye on my gear."
Phoenix media manager Russel Gray said it was the first time anything like this has happened at the club's training ground.
"The crazy thing was there was some money hanging out on one of the benches and that got left alone," Gray said.
"We were actually filming there at the time and hopefully they can blow up the picture and use that.
"This is the first time anything like this has happened. The gates are normally closed but they are left unclocked so that when the balls go over the fence they can run around and get the balls. But the first time anything like this has happened at Newton Park in eight or nine years.
"There's always someone wandering around, I'm normally wandering around so they would have had a very short window of opportunity."