The 23-year-old England winger admitted he had considered quitting the Riverside after being jeered by fans during the draw with Spurs 10 days ago.
However Southgate said: "He has never asked to leave. His heart is here and he's a young player who has been a terrific talent for us. He has got us so many points and scored so many goals and created so many goals for us. He is a match-winner for us."