It had been reported that Downing had held talks with Southgate about leaving Teesside after growing tired of some fans' booing of him.
However, Southgate hit back at the stories, telling the Evening Gazette: "He's never asked to leave. No way has he been in and asked me to leave - he's not been in to see me about anything.
"I spoke to him after last weekend's game, but that's all.
"All I have expressed to him this week is the belief I have in him as a player, and that he has produced time and time again for us. The stick he has taken, he takes it on the chin.
"His heart is here and he is a young player who has been a terrific talent for us and has got us so many points and scored us so many goals and created so many goals for us - he is a match-winner for us."