Arnautovic has not featured in the Bremen team since April after he was suspended by the club after he was caught speeding by police.
The agent for the Austria international, Roger Wittmann, told Bild he has been in touch with Neil Lennon to tell him Arnautovic is staying with Bremen.
"Marko will not transfer there, I have already informed Celtic's manager," Wittmann said.
Werder's director of sport Thomas Eichin has said Arnautovic has a future at the club - providing he behaves after other misdemeanours including a training ground bust-up in March with a Bremen team-mate.
"He is an important, high quality player. If he brings 100 percent of his quality to the pitch, then he is a big plus for us," said Eichin.
Celtic manager Lennon was asked about Arnautovic following the 2-0 victory at Aberdeen and replied: "We are interested in the player but whether there has been a bid in or not, I can't confirm, I wouldn't have thought so."