The Bundesliga outfit have been linked with a move for Roque Santa Cruz, who has returned to parent club Manchester City this summer following a successful loan spell in Spain with Real Betis.
Santa Cruz could find opportunities difficult to come by at the Etihad Stadium, with Sergio Ageuero, Edin Dzeko, Carlos Tevez and Mario Balotelli all vying for starting spots.
Another player currently struggling for opportunities at his current club is Srdan Lakic, currently with Wolfsburg, who is understood to be keen on remaining in the Bundesliga if he does move anywhere.
And Allofs has fanned the flames of speculation by admitting that Bremen are in market for players capable of finding the back of the net in the upcoming 2012/13 season, though he says the club are keen to recruit a proven performer.
"There is definitely one striker we are looking at. It's an experienced striker, one that has already shown his qualities," he said.
"We would not benefit if we just add one more striker for the sake of it. We need a good one that makes us a better team. We do not need an 18-year-old. We have enough youngsters in the squad."