The Times says Tottenham and Everton have been long-term admirers of Downing, but Southgate has made little secret of his determination to reject their advances.
"He is very, very settled in his mind that he wants to play his football here and he is an incredibly valuable part of the team," Southgate said.
"I know negotiations have been going on for quite a while, but what we have tried to do with all the young players is keep rewarding them every year or two years for their performances and get their contracts sorted out before it gets to the stage where they have only a few months left.
"With Stewart, we are talking about this, but he still has two years-plus to go. We see it as one of our priorities, but in terms of the timescale, there is still time to negotiate with him."