The 29-year-old's current deal runs out next year and he maintains he wants to remain at the club.
But Bremen, Champions League participants last term, missed out on Europe altogether for the coming season and Allofs admits money is tight.
"We have told Tim that, because of financial reasons, we can't extend his contract at the moment," Allofs was quoted as saying by the Bild newspaper.
Wiese, who has won three caps for Germany, has been linked in the German press with a move to Wolfsburg.
The player himself, though, insists a move is out of the question.
"That is absolutely not on the agenda," he told the club website. "I have a contract at Werder until 2012, which I would like to fulfil and I can also see myself extending it again."