The FA are so convinced that the Three Lions boss will deliver success that a decision has already been made to open talks over a new long-term contract.
Southgate’s current deal takes him up to the next World Cup in 18 months’ time. But the FA want to fend off any interest from club sides and have informed him that they want him to carry on regardless of England’s performance at Euro 2020.
Chief executive Mark Bullingham said: “Gareth knows exactly how we feel about him. He knows that we think he’s doing a great job and we’d like him to carry on.
“We would love him to carry on, for sure, beyond this contract.
“I think he’s doing a brilliant job. We’ll get into that formal conversation after this tournament.”
Southgate was briefly linked with the Manchester United job after Jose Mourinho was sacked in 2018, but the role went to Ole Gunnar Solskjaer.
There have been no serious approaches from leading clubs, but the FA are aware his reputation will soar if he can lead England to the latter stages of the Euros.
Bullingham added: “We’re in a competitive world. I’m sure his name gets bandied around for every job, but as far as I know he’s really committed to the job and I think he’s doing it brilliantly.
“From our point of view he has our full support and he knows how we feel about him which is the most important thing from our side.
“I think he’s got a brilliant long-term career in football and I know he might have aspirations longer term.
“Our support is unwavering. 100 per cent unwavering. We are 100 per cent behind Gareth. We want him to carry on. Regardless of Tuesday. Regardless of the group stage of the tournament we would have wanted him to carry on, not just in [major] tournaments but if you look at Nations League as well, he did brilliantly in that.
“He’s got our unwavering support because we think he’s doing a brilliant job on and off the pitch. Every game we go into we want to win and we think he gives us the best chance of doing that.”