Southgate is happy with the progress Boro are making and has hinted that he would like to extend his contract.
He told the Sunday Sun: "This is not my football club, it's the chairman's football club and the fans' football club. I'd love to be here as a long-term part of that, I'm not here to just pass through.
"I want to build something. We're here for a long time, and if we are we'll be doing it well and having success."