Many had suggested that it was between the Manchester City keeper and the Manchester United forward for the role, however Hart feels that the position is already Rooney's.
"I've not thought about it at all," said Hart.
"How the captain is chosen is the manager's decision. I've got a big responsibility to keep my place in the team for club and country.
"If I do get the nod, I'll try and give as much as I can in terms of helping the team. But I think it's between Wayne Rooney and Wayne Rooney if we are going to go on experience and how captains have been chosen in the past."
Rooney has 76 England caps.