"We have received an unacceptable offer and we will not allow negotiations to open," Werder sports director Klaus Allofs told the SID news agency.
Financial details of the bid were not disclosed but German media reported that a €16-million price tag had been placed on Özil whose contract with Werder expires in June 2011.
Real Madrid coach Jose Mourinho admitted his great interest in the 21-year-old.
"His club said no. No we will have to see what happens. It would be great if he could join us," said Mourinho.
Ozil has been the recent target of clubs such as Arsenal and Manchester United.
The midfielder, who joined Werder Bremen in January 2008 for €4.25 million, impressed during the World Cup this summer in which Germany finished third.
It was also reported at the weekend that football's world governing body FIFA is considering scrapping drawn games from the group stages of the World Cup finals.
The organisation's chief Sepp Blatter Focus magazine he wanted to put an end to defence-minded teams playing to get a draw in the early games of the sport's showcase tournament.
"We are considering doing away with draws in the first round ... and also ending extra-time play," he said.
"If there is no winner at the end of 90 minutes of play, we would proceed directly to penalty kicks."
Another possibility, according to Blatter, would be to revive the Golden Goal scenario whereby if a match is drawn, the first team to score a goal would be the winner.
That was used in the 1998 competition in France but was abandoned four years later when the finals were held in Japan and South Korea.
The next World Cup will be held in Brazil in 2014.