Southgate's side booked their place at next year's World Cup in Qatar with a 10-0 thrashing of San Marino on Monday.
Reports over recent weeks suggested Southgate is set to sign an extension to his current contract with the Football Association, which runs out at the end of the World Cup.
Southgate had refused to be drawn on the situation while England were focused on securing their qualification.
But after their biggest ever victory in a competitive fixture, he admitted he sees no reason why his reign will not be extended until at least Euro 2024.
"When you work with staff like I work with and with a group of players who are as receptive and have the talent that we have then that's clearly very enjoyable," Southgate said.
"So there's been no other reason for not sitting down other than the fact that we felt it was right to concentrate on the European Championship and to get this qualification done.
"Now it's an appropriate time to be able to sit with (FA technical director) John (McDermott) and (chief executive) Mark Bullingham and go through everything - but I'm not expecting for that to be complicated at all."
England are still waiting for a first major trophy since the 1966 World Cup, but Southgate has them trending in the right direction after a memorable 2021.
Having led England to the final of Euro 2020 in July and the World Cup semi-finals in 2018, Southgate's men will be genuine contenders in Qatar.
But England's World Cup challenge will be complicated by a lack of preparation time.
The Premier League announced last week it will pause the season after the weekend of November 12-13, with the World Cup kicking off just over a week later.
Whereas most pre-tournament camps would allow time for several warm-up fixtures, the scheduling means Southgate is not expecting to play a friendly before the World Cup.
"Ahead of the tournament, I'm not sure what that's going to look like for anybody but I would think it's really unlikely that teams are going to be able to play a friendly," Southgate said.
"If you think about the Premier League teams playing on a Saturday or Sunday then you'd need three or four days before you'd play and I think you normally have to be in the country five days ahead of a major tournament anyway.
"So it's going to be the teams that adapt best and we've got some experience of that with the Nations League and the European Championship where we had so many players involved in the Champions League finals, so at least we have been through that experience."
Standout matches today