The Turkey international, who is expected to leave the club before the closure of the transfer window, scored in Saturday's 3-0 at Swansea after coming on as a substitute following his return from international duty in midweek.
Southgate said: "Yes we know the position, he is looking to return to the Premiership, but the bottom line is - no club has tabled a bid.
"Until that happens he's a Middlesbrough player.
"The transfer window is open for a further two weeks and we expect interest, but as of today, we have heard nothing."