Pizarro, 33, has been linked with a return to the Bundesliga giants, for whom he played for six years before joining Chelsea in 2007.
The Peru international initially joined Bayern from Bremen in 2001 and, while he has an excellent record at both clubs, Allofs is worried that this time out he would struggle to get a starting spot.
"Bayern is not the ideal club for Claudio Pizarro," Allofs told Bild. "Here he is a key player, the one who leads the line and scores goals.
"Would that be the case at Bayern?"
Bayern’s first-choice strikers are Mario Gomez, who has already passed the 40-goal mark this season, fellow Germany international Thomas Mueller and Croatia forward Ivica Olic, although the latter is set to leave this summer.
They also tend to play with two very advanced wingers in Franck Ribery and Arjen Robben.
But, despite the competition, Allofs conceded that Pizarro could exercise his right to terminate his contract in the summer, particularly if Bremen - who lie eighth with three matches remaining - fail to qualify for Europe.
"I think his decision is dependent on European football - I believe that our qualification or otherwise is the key for whether he stays or goes."