The 35-year-old Australian is out of contract at the end of the current season and could leave the club on a free transfer unless he signs a new deal.
Asked if there had been any subsequent progress, Southgate said: "Not at the moment, no.
"Mark's contract is up in the summer but it's one of those situations where he is playing so well, you don't want to upset things.
"But it is a situation I am conscious of. He didn't want to talk about it until January at the earliest.
"I have got a very good relationship with him, but I need to talk to him and see what his thoughts are as much as anything."
Schwarzer joined the club in a £1.5million move from Bradford in February 1997 and has been first-choice goalkeeper ever since.
