Rooney, 30, has started Manchester United's last three games on the bench amid an ongoing debate about the best place for him to play as his physical powers wane.
Both club manager Jose Mourinho and Sam Allardyce, Southgate's short-lived predecessor, announced plans to deploy him as a number 10, although they then used him in more withdrawn midfield roles.
"I don't want to go against Jose, but I think Wayne can play any number of different positions," said Southgate, who has kept faith with Rooney as captain.
"The only thing I would say is I go back to one of the things we work on with the team: in and out of possession, tactical discipline, positional discipline.
"So whatever position you play, it is clear to the players that they understand that fully."
Rooney, England's record scorer (53 goals) and most-capped outfield player (116 caps), played in midfield under Roy Hodgson during England's ill-fated Euro 2016 campaign.
Mourinho subsequently vowed Rooney would "never" play for him in midfield, but he has featured there at times for United this season.
Allardyce also expressed an intention to use Rooney further forward, but the former Everton player conspicuously took up deep-lying positions during last month's 1-0 win in Slovakia.
Citing Rooney's vast international experience, Allardyce said "it's not for me to say where he's going to play".
Southgate conceded Rooney's lack of playing time with United was "not ideal" and refused to confirm if he will start Saturday's World Cup qualifier at home to Malta.
"I'm not prepared to give my team to the opposition, but I'm clear in my mind how that will play out," said Southgate, previously England's Under-21s coach.
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