The Bremen boss is certain that the Bavarians have yet to wrap things up with the veteran striker, after reports claimed a deal had been struck between club and player
Earlier on Thursday, TZ reported that the veteran, who will be out of contract in the summer, had accepted an offer from the Bavarians, and had even begun his search for a house in Munich.
However, Allofs insists that he knows nothing of the alleged agreement, and that he would be the one to find out.
"I do not know anything about it," he told Weser Kurier. "Pizarro made it clear that [Bremen] would be first to know about any news regarding this topic."
Bayern have long been in the hunt for a striker, with Ivica Olic set to leave the Allianz Arena this summer. The German giants made an offer for Athletic Bilbao's Fernando Llorente, which was rejected, and also looked at Olivier Giroud and John Guidetti, as well as Pizarro.
The 33-year-old previously plied his trade with Bayern from 2001-07, and the Munich giants have been closely linked with him in recent weeks.
Having previously scored 158 times for Bremen and Bayern combined, Pizarro is the most prolific foreign-born player in Bundesliga history. He and Bremen will take on Bayern on Saturday, with kick-off scheduled for 15.30CET.