Reports have suggested that Spurs are prepared to pay £10million for the 23-year-old Teesside-born player, but Southgate insists there have been no bids received in the current transfer window.
Southgate said: "I was very interested to see Stewart's agent on TV telling us what may or may not happen.
"I don't think it's been very helpful. But that's football. Everybody wants to have their say publicly.
"As far as I am concerned I don't want anything to happen. Stewart is a player I don't want to lose.
"He is a very influential player for us and he is our top scorer."
Southgate added: "We still haven't received a bid for Downing and I hope it doesn't happen before January 31.
"He is a player I think the world of. I want him to be part of our future. I see him as part of our plans."