Southgate refused to rule out making an attempt to ask Rooney to perform a U-turn on this week’s decision to retire from international football.
Rooney called it quits despite looking revived since returning to Everton and making a promising start to his second Toffees spell with two goals in two games.
But a strong season ahead of next summer’s World Cup, which the Three Lions are firmly on course to qualify for, could persuade Southgate to pick up the phone.
He said: “I suppose that we have to see where he was at, where the squad was at, where everything else was at.
“It would be foolish to say ‘no’ because anything is possible.
“Really part of that question should go to Wayne, but I think you’ve also got to respect his decision and the thinking behind that.
“But have I seen players change their minds? Well yes, I think we all have.”
Southgate also backed plans for Rooney’s career to be honoured, with FA discussions on how best to mark his achievements under way.
He said: “Absolutely we should be recognising his career with England, and showing appreciation.
“I know already there is discussion around that and discussion about how we may keep him involved with England just as we are talking to Frank Lampard and Steven Gerrard and others as there is value to that experience being passed on.”
Southgate admitted he had “not enjoyed” omitting Rooney from his squads.
Doubts over the forward’s international prospects really began to grow after boss Southgate axed him from his last two Three Lions parties.
But Rooney took matters into his own hands by quitting England for good on Wednesday, sparing Southgate some of the flak for why the 31 year-old’s record-breaking international career is now over after 119 caps and 53 goals.
Asked if the fact it was the once-again Everton star’s call stopped him feeling like the man who shot Bambi, Southgate said: “Well, I’ve taken no pleasure from not selecting Wayne.
“So, would I have preferred to have had a relationship with him where he was in the team all the time and playing at a world level? Unfortunately I was the one who got him when he was making the decision that he’s making.
“I think I’ve made decisions for the right reasons and I think I’ve communicated them to him always in a respectful way. You can’t do any more than that. So, I sit comfortably with that but I’ve not enjoyed that, I’ve got to say.
“I say that because not only having played with him and respect what he’s given but also respecting the qualities that he’s got.”
Southgate called Rooney and planned to include him in this squad following his return to form since rejoining his boyhood club. But before he could reveal his intentions, the player dropped the bombshell that he had already decided to call it quits.
Southgate explained: “My intention was to call him up, but also I never assumed that when somebody has been out of the squad that that’s what they might want to do.
“I was going to discuss that, on form, he deserved to be in the squad. Could I see him definitely starting? No, I couldn’t give that guarantee. But do I see the value of a senior player and what he may add in terms of experience and developing some of the other players? Definitely. But I never got to go that far.
“I did discuss that with him after and he was appreciative of where the idea was. Would that have worked? Who knows? It could have been a good call or a bad cal,l but I think he has shown with Everton what that may look like.
“Stoke at home, they were 1-0 ahead and [he had] the ability to keep the ball and take the pace out of the game. He is in a different place, form-wise, in terms of his hunger and his desire to get in the box and all of those things.”