Sanogo has made just one start in the Bundesliga for Werder this season.
The 26-year-old Ivory Coast international has been linked with Marseille, Newcastle, Portsmouth and Blackburn.
“If they do not want me any more, they should be fair and tell me,” Sanogo told reporters.
“I don’t feel any trust in me since coming back from the African Cup of Nations last year and I need to get more playing time.
“I would love to stay on, but if I do not get my games I have to move on. I would even join a smaller club.”
