Rumours earlier this week circulated that Southgate could be the next Premier League manager to lose his job after one bookmaker suspended betting on such an occurrence.
Southgate is not surprised by the speculation due to Middlesbrough's struggles to avoid relegation, but he insists he has the full backing of the club's board.
"I know the situation here, of course, when we are where we are in the league people are going to question your position, but we get on with our jobs," said Southgate.
"We have the complete backing of everybody here, everybody knows the difficulties of the job and we will give it every ounce of energy, until we are told otherwise, to do the job."
TestMiddlesbrough face a massive clash with fellow strugglers Stoke this weekend and Southgate has challenged his troops to pick up three points at the Britannia Stadium as they look to climb out of the drop zone.
"It is a big challenge for us. Can we go to Stoke and take the points because we have not done enough on our travels,"
"We know stoke are very strong at home and we have got to be up for the battle."