Martin O'Neill has warned Nicklas Bendtner over his off-field behaviour.
Bendtner was arrested and bailed with Sunderland teammate Lee Cattermole last week on suspicion of damaging cars after a night out in Newcastle.
"He is pretty popular in the dressing room, you know. I just want him to be popular in the manager's office as well," O'Neill said. "He can manage that by doing two basic things. Win us some football matches and behave himself. Then he will be really popular with me.
"My own view is that behaviour on and off the field is of paramount importance because of the expectation of footballers, particularly in this league where they're in a very nice position financially.
"I think they kind of owe a debt really and that's something that we would like to see happen at this club."
O'Neill insisted that the club are taking the matter seriously.
"The police have to finish their inquiries, it's a very serious issue and one that won't be overlooked by the football club," he said.
"The players and the managers, I believe, have extra responsibilities at football clubs.
"I believe that someone like Nicklas can get a few goals and that would breed a bit of confidence."
Sunderland are currently 17th in the Premier League, one point above the relegation zone.