Werder Bremen have hit out at constant speculation linking Serge Gnabry with Bayern Munich after his hat-trick on his Germany debut made the forward red-hot property.

The 21-year-old joined Bremen from Arsenal for a bargain five million euros ($5.3m) in August after signing a four-year deal and has made an immediate impact for club and country.

He won silver with Germany at the Rio Olympics, has scored four goals in nine league games for strugglers Bremen and capped his senior debut at San Marino last Friday with three goals.

He was the first German to score a hat-trick on his international debut in 40 years and was set to make his second appearance for the world champions in Tuesday's friendly against Italy in Milan.

But Frank Baumann, Bremen director of sport, says he is annoyed by persistent rumours -- which the club has repeatedly denied -- that Gnabry's contract has a release clause allowing him to join Bayern.

Baumann has even been compelled to quash rumours of a transfer in January's winter break to Bayern, who have a tradition of snapping up talented homegrown players.

"You have to ask yourself why these rumours remain in circulation," Baumann told website spox.de.

"They appeared the day before the signing, were then repeatedly denied by us and are still discussed to this day.

"That's a pity because we made our position clear. I can't explain why these rumours still keep appearing."

Bremen are third from bottom of the German league with Bayern top.

When Gnabry signed for Bremen, there were rumours that Bayern had paid the transfer fee and would then loan him back to their fellow German club.

"There aren't any agreements with other clubs. Serge Gnabry is our player. We have bought him," insisted Baumann at the time.

So swift has been Gnabry's rise to the Germany squad that he admitted he thought it was a hoax when the call came from head coach Joachim Loew.

"The coach called me up but I had to think about it for a bit whether it was true or not," he told German media company RND.

"There are so many hoax calls from radio shows and I really did not want to be a victim of that."