England's manager until the conclusion of the European Championships in four years' time.
According to Sky Sports News, there is a belief that he should stay on and that he will inform the FA before Christmas.
After England's elimination from the World Cup, he told the FA he needed time to think about his future.
"We've done that after every tournament, and that's the right thing to do, because these tournaments take a lot out of you," he said. I don't want to be four, five months down the line regretting my decision. Everybody needs to get that right.
After talking to his family, it is believed that he will see out his contract until the conclusion of the European Championship in Germany in four years' time.
England reached the last eight of the World Cup, the final of Euro 2020 and the semi-finals of the World Cup under Southgate's watch.
Sky Sports News is led by a senior reporter.
The FA is in a very difficult position if it is left now.
England's next game is against Italy in Naples in March, which is an incredibly difficult game that could decide England's qualification for Euro 2024. That's why they needed a quick decision from the man. They wouldn't put pressure on him, they would give him time to think.
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It's great news for the England players. Most of them wanted him to stay on because of the atmosphere he's created within the group and the success he's helped engender.
The FA are desperate for him to stay on because he has done a good job and there is no obvious replacement.
He thrives in the structure and is an FA man. There is no heir apparent. The FA has time to plan for the future.
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Gary Neville is a commentator for Sky sports.
I think there is no English person who has more experience at major tournaments, junior tournaments and playing for his country than him. I think he should be in the system to design the future.
"He has been there for 10 years, we've had great success with the women's teams, with the younger teams, and I think we've had really good success with the men's team." I don't want him to leave the FA after his coaching role.
England got rid of Bobby Robson. Terry Venables was removed from the scene in 1996. After those tournaments, it didn't go well, but I think Gareth is doing a great job, and one more tournament for me feels right.
gareth is an honest man with integrity who will make the right decision for the FA. It feels to me like 18 months is the right amount of time for a succession plan to be in place.