Rooney, 31, was left out of the squad in March for matches against Germany and Lithuania and he has again been left out for the upcoming fixtures against Scotland and France.
Rooney has fallen down the Old Trafford pecking order and while he started United’s last five Premier League games, he was largely part of a second string lineup as Mourinho’s focus turned to the Europa League.
He was left on the bench for the first leg of the semi-final against Celta Vigo, before managing less than 10 minutes across the second leg and last week’s final defeat of Ajax in Stockholm.
England’s record goalscorer looks set to depart United this summer, with suggestions of a return to Everton or a big-money move to China.
And according to Southgate, continuing to formulate his plans for next year’s World Cup in Russia, the door isn’t completely closed.
“It doesn’t have to be,” Southgate said, when asked if Rooney’s international career was at an end. “From Wayne’s point of view he hasn’t played very much this season.
“Wayne’s got some decisions to make this summer, but the hope is that he’s back. A player of his quality there is no way we would dismiss him.
“You want your players playing in the biggest possible games.
“I’ve no idea what the future is for Wayne at Manchester United so it’s impossible for me to comment if he’s part of the plans or not.
“I’ve spoken to him in the past but not this time – I think there’s only so many times you can speak about the situation.
“I’m conscious from his point of view that it’s always a big story when you don’t select him.”
Nathaniel Clyne has pulled out of the squad for the matches at Hampden Park and the Stade de France with a back injury.
“There are a lot of potential leaders emerging from this group and that’s good because there’s always been a focus on one person and an over-reliance on one person,” he added.
“We’re in a position where we can go a number of different ways with that.”