The 24-year-old has one year left on his current contract at Colchester.
And Southgate said: "He's a player that I'm interested in.
We've been in negotiations with Colchester and we feel we are close to being able to do some sort of a deal there.
"Hopefully something might happen over the next couple of days.
"We need players of Premier League quality but I want players who have played in the Championship and who have a hunger to push on and a desperate desire to play in the Premier League.
"We want a mixture of hunger, energy and quality."
Colchester have also confirmed that they are in talks with Boro over dead-ball specialist Yeates, but are still to agree a fee.
"It will take a sizeable commitment from Middlesbrough to prise him away from us," Colchester's chief executive Steve Bradshaw said.
"We are desperate not to lose Mark because we feel he is part of our future.
"We will do everything we can to keep him. But the chairman doesn't want to stand in the way of players if they get a fantastic opportunity."