There was no list of high-profile applicants when Southgate replaced Sam Allardyce in 2016, just months after England had embarrassingly crashed out of the European Championship at the hands of Iceland.
Since then, the former Three Lions defender has led his country to a semi-final at the 2018 World Cup, a third place in the inaugural Nations League and came within a penalty shoot-out of delivering Euro 2020 success last summer.
However, a run of poor results recently has left England without a win in six games and seen Southgate come under pressure for the first time.
While the 52-year-old has a contract until 2024, there have been some big-name coaches who have said the England job would interest them.
Former Tottenham and Paris St Germain boss Mauricio Pochettino recently told the Athletic he was “open” to the idea, while it has been reported that ex-Chelsea coach Thomas Tuchel is also keen on the role.
Asked if it was a compliment to the work he has done that there are people courting the position, Southgate replied: “Maybe we’ve made the impossible just look possible.
“Look, maybe we’ve made it look possible and it’s exciting for other people and I can understand that. We want England to be competitive for years to come and I believe that our academy system has got that.
“I think there are challenges within that because we’re back to 31 per cent of the league being eligible for England and only four or five exports of a high level so there are still some challenges for us in terms of development of players and opportunity for players.
“But we have also got some good players and we should be competitive for the next six, eight years with this group.”
Southgate revealed that a quick search of the internet also gave him a clear reflection of the level England should be targeting in the future, having been left scrolling through the achievements of their rivals.
“Of course, the results in the summer were the thing that created the tension around September in particular,” he added.
It is my responsibility to remind the players that actually there is a lot they’ve done well and coming into this tournament, they shouldn’t be focusing on the recent past
“It is also my responsibility to remind the players that actually there is a lot they’ve done well and coming into this tournament, they shouldn’t be focusing on the recent past.
“It is hard to talk about form because you are always six weeks, two months between games in international football, so what actually is form?
“What there is, is pedigree. We want to be a Germany, who when I was looking at their Wikipedia page: (World Cup) four golds, four silvers, four bronzes, European Championships three golds, three silvers, three bronzes.
“Yeah, our page didn’t quite look like that but we’d love it if it did in 40 years’ time and that should be our aim, to be consistently challenging.”
England’s campaign opens against Iran on Monday as they look to put down a marker for the remainder of the tournament.
Southgate believes his current crop have matched England’s best sides of the past and feels history may have been kind to some previous tournament displays.
“We’ve had some great squads of players and we’ve had squads of players with world-class talents in almost every position,” he said.
“So I think the strength of this group has been the team. I think at times we’ve played football that has matched any of those teams. I played in a team in 96…everybody will remember the Holland game but there was also a Switzerland game and a Spain game and half a Scotland game.
“So I think that’s always the way. I remember watching the re-run of the 1966 final, I think we were 3-1 up and the team passed backwards and the crowd were booing.
“Plus ca change as they say. It is what it is. We’ve got to make sure we know what our intent is, what our mindset is.”