"We've not even spoken about it and everybody who's here is very settled and everybody's looking forward to the start of the season."
So not a problem then. But, Southgate admits, not a surprise either.
"Stewart was excellent for England in the summer so that's bound to raise his profile," he said.
"We've said all along that he's a fantastic player, we've known his quality. Inevitably he'll be linked, whether it's genuine or mischievous.
"But he's signed a long contract in the middle of last season, he's very very happy here and we want to build a team that encourages him to be here even longer."