The 53-year-old has been in charge since 2016, taking his side to the 2018 World Cup semi-finals, the Euro 2020 final and the 2022 World Cup quarter-finals in Qatar.
His contract is due to expire in December but the Football Association are keen for him to remain as manager for the next World Cup in 2026 in USA, Canada and Mexico.
However, Southgate told German newspaper Bild, external that failure to win a trophy in Germany could see the end of his stay.
“If we don’t win, I probably won’t be here anymore. Then it might be the last chance,” he said.
“If we want to be a big team and I want to be a top coach, then you have to deliver in the big moments.”