Viduka has been linked with Premiership rivals Tottenham and Newcastle.
Southgate told the club’s official website: “I’m keen to move ahead with it as quickly as we can. It’s important that we keep the players that we have.
“We haven’t got things underway yet but the games have been coming thick and fast and Mark was away with the Australia squad last week too.
“We want to get it wrapped up as soon as we possibly can. I think everybody wants to sit down and start discussions.”
