The Peruvian - the Bundesliga's all-time top foreign goalscorer with 176 goals - was released earlier in the close-season when his contract expired.
He has yet to find himself another club, although he insists that is not down to a lack of interest.
"I've had a few, but not yet the right one," the 36 year-old said, quoted by Sport1.de.
"I don't have any rush, though. I'm keeping my options open."
One of the offers he is understood to have turned down is from Bayern's city rival 1860 Munich - a move which would have meant his family did not have to move away from the Bavarian city.
"I certainly can't go to '60," he said. "And as a former Bremen player, I couldn't go to Hamburg either, in my opinion."
Pizarro does not wish to drop to the second division either, but that does not mean he will be remaining in Germany. He would consider other offers, adding "as long as it is a top division".
