Rooney, 31, missed United's 4-0 defeat by Chelsea on Sunday through injury.
He was a substitute for the previous three Premier League games and has scored only once this season.
Southgate, who omitted Rooney for England's World Cup qualifying draw in Slovenia this month, said his leadership was "hugely impressive".
Southgate added: "He's the England captain and, although he didn't start in Slovenia, to me he is a hugely influential figure in that group and that won't change.
"I thought his leadership qualities in the 10 days with us shone through. I could see how he's held in the eyes of the rest of the players and the positive influence he has in that environment."
Southgate's initial four-game spell in charge ends with a World Cup 2018 qualifier at home to Scotland on Friday, 11 November and a home friendly against Spain on Wednesday, 15 November.
"Let's see what that scenario is," Southgate said of the role Rooney would be likely to play.
"I haven't spoken to him since the camp but I'm always conscious players are back into a run of fixtures with their clubs.
"I will pick up with him and the others later."