The Peruvian striker joined Bremen last summer on a one-year loan deal after failing to establish himself as a first-team regular at Chelsea.
Chelsea's former coach Luiz Felipe Scolari deemed him surplus to requirements but it remains to be seen whether new boss Guus Hiddink would consider bringing him back to Stamford Bridge.
"The decision will take time and they will be waiting to see what happens. Who will they buy, who will be moved on," Bremen's general manager Klaus Allofs told Bild.
"We have to be prepared to wait on a decision for quite some time. Potentially up until late August.
"But we have an agreement with Claudio. He wants to stay with us as he feels happy at our club. That is certainly increasing our chances at this end."
Pizarro is Bremen's top scorer with 10 goals to his name so far this season.