The 31-year-old has come in for criticism in recent weeks after pictures were leaked to the media showing him looking worse for wear at the England hotel in the middle of the November international break.
Speaking to the media today for the first time since being named permanent Three Lions boss, Southgate said that Rooney remains captain for now but hinted that he wants to "give other people opportunities to lead" in the future.
"Wayne Rooney is the England captain," he said. "I said that at the beginning of the interim period. I've also only selected him to start in two of the four matches we've had, so it's obviously not a case that Wayne expects to play every game.
"I think it's important that we develop more leaders in that group over the coming months. When I played for England, particularly in 1996, there were captains throughout the team. If we're to be successful in the next few years, developing leadership and resilience is one of the key areas, so we've got to develop that and give other people opportunities to lead in different ways.
"Wayne has played an important part for England up to this point. I'm sure he can do that in the future but we have to develop others."
Last week The FA reportedly decided not to charge Rooney with misconduct for his behaviour while on international duty.