The American, who joined the club in January, will see his short-term deal expire in the summer but he has refused to confirm whether he will be playing his football at Hillsborough next season.
"I have signed until the end of the season and you never know," Onyewu told Sky Sports News. "Things can move very quickly in football so I never like to rule out any options or burn any bridges before I need to.
"A player of my personality and my character, I try to work towards the best always and try to always push myself to a higher level.
"We will have to see what happens after this season, if another situation comes up or if Sheffield is the best situation for myself."
Onyewu moved to Wednesday following an unsuccessful spell with Queens Park Rangers.