The Scotland striker has already suffered relegation with Burnley and Wolves.
A source close to the player told the Sunday Sun: "Steven was top scorer with both Burnley and Wolves in the seasons that they were relegated and he does not want to see it happen for a third time.
"And he is confident it will not happen with Sunderland.
"Some players might have had a release clause written into their contract if their club was relegated but nothing was further from Steven's mind.
"He could not be happier at Sunderland with the poor recent results the only black spot."