The 48-year-old led the Three Lions to the World Cup 2018 semi-final in July, their first major tournament semi-final since 1990.
His current contract expires in 2020, and speaking before Tuesday’s friendly with Switzerland, Southgate remained coy on his future beyond that date.
“Well, first and foremost, I am 100 per cent focused on this job, nothing else,” he said. “I am under contract, I have two years.
“You know that leads to a European Championship, which we have games at Wembley, which is going to be a brilliant experience. That is my pure focus.
“I know absolutely what comes with the job so anything that suggests there’s a problem with what surrounds the job, and the focus and attention of it, absolutely no problem at all.
“I want to be in games that matter.
“I believe I’ve been through an experience that is as pressured as you’re ever going to face at any club or international team in getting through a World Cup, so I’m totally comfortable with that, and what’s beyond that is to be decided.
“For me, I’m under contract, I’m enjoying the role, I love the challenge of it and that’s it really.”