The England captain has already been dropped at Manchester United this season by Jose Mourinho and interim England boss Southgate is facing calls to do likewise.
Rooney was jeered by some fans at Wembley on Saturday during England’s 2-0 win over Malta.
Southgate is expected to stick by his captain for tomorrow’s World Cup qualifier in Slovenia.
But he says he won’t hesitate to make the big decisions if he feels they are necessary.
“I’ve got to make decisions which are right for the team and whenever you select a team, with England, you’re going to leave some guys on the bench who are playing every week in the Premier League for their clubs,” said Southgate.
“You have to be prepared to do that – that’s part and parcel of the job.”