Wheater's current deal expires at the end of the season and a string of impressive performances have drawn admiring glances from elsewhere.
The interest is hardly surprising as the centre-back's rise to prominence this season has seen him force his way into the England Under-21 set up.
"David's having a terrific season," said Southgate.
"The maturity he has shown and the way he's standing up to the challenge of playing against top international players will stand him in good stead.
"He's at a lovely phase in his career where he just goes out and plays and isn't worried about anything else. It's great to watch.
"I'm confident he will be signing a new contract, and pretty soon too.
"He's a Middlesbrough boy and loves playing for the club. We give young players a chance more than other clubs do."
Wheater grabbed his third goal in 19 Premier League appearances during the 1-1 draw with Blackburn on Saturday and admitted he has surprised even himself with his success.
"I can't really believe how well it's going for me personally," he said.
"I didn't even expect to be here this year. I thought I'd be out on loan.
"But here I am in the team and hopefully I'll stay there. I could be top scorer the way things are going.
"I'm only one behind Stewart Downing and I'm after him."