The 19-year-old has made 21 appearances in the Premier League for The Toffees this season and has been named on England's stand-by list for this summer's World Cup.
"There is not a hint of arrogance about him, he's a dream to work with and so grateful for the opportunity all the time," The Express quotes Southgate as saying.
"His composure on the ball is fantastic and we're looking for defenders to play out. His experience at full back probably helped that. Like any centre back he will have to learn the defensive positioning that only comes with experience, but nothing fazes him, nothing with us, or Everton.
"I had a great chat for him on the phone the other night. He was chuffed for his family, he's just so thankful and it is a pleasure when you work with lads like that."
Stones joined Everton from Barnsley in January 2013.