The 30-year-old, who has endured a difficult season at the club level, attracted criticism for his performance in the 2-2 draw with Scotland last week.
When asked who is his number one keeper, England boss Southgate said: "Joe Hart. Next season we don't know who will be playing at which club and who will be in form.
"But Joe has been excellent for us. The goals on Saturday were the first he'd conceded in qualifying, and we owe him for Slovenia.
"His contribution around the group has been excellent since I've been manager."