Middlesbrough defender Emanuel Pogatetz looks set to be sidelined until Christmas following a cartilage operation.
Robert Huth, Matthew Bates and Chris Riggott are also on the injury list, but Southgate is staying positive.
He told the Evening Gazette: "I'd be worried with five centre-backs out if we didn't have any cover, but we have cover.
"Andrew Davies and David Wheater have done well in the pre-season matches. I was delighted with both of them against AZ Alkmaar.
"Andrew has a fair bit of Premier League experience and while David hadn't played that many games, he is a promising lad and he has done very, very well in pre-season."