Bremen chief Klaus Filbry had claimed that the Austria winger had been the subject of a tentative enquiry from the Ukrainian giants.
But Schaaf insisted that the former Internazionale forward, 23, is very much in his plans.
“I know nothing of this,” Schaaf said. “We have had a great season with Marko so far and are happy to continue with this.”
Arnautovic has a reputation for poor behaviour, which saw him only spend one season at Inter following his loan move from FC Twente in 2009.
But he has improved this campaign, scoring five and creating five in 15 Bundesliga matches, and without any of the attitude problems that marred his early career.
His contract runs until next summer, however, so unless Bremen extend his current deal they could seek to cash in on his undoubted but unpredictable talent.