The Peruvian's contract expires at the end of June, after he activated an option to terminate his current deal a year early.
Bayern Munich were thought to be interested in their former player, whose delaying tactics must end, according to Allofs.
"I believe him when he says he has not yet made up his mind, but he has got to reach a decision now," Allofs told reporters in Bremen.
"We are not playing in the Europa League so he must be able to make up his mind in the very near future.
"It should not drag on for three or four weeks."
Pizarro ended the season on a high with two goals in their 3-2 defeat to Schalke at the weekend, but few others were celebrating inside the Weser Stadion.
"After this second half of the season, all you can say is 'thank God that's over'," said captain Clemens Fritz, who recently extended his contract.
And after the worst second half of a season in the club's history, with just 13 points in 17 games, changes can be expected in Bremen this summer.