The Peruvian attacker is happy with life at Bayern Munich and is keen to stay at the Allianz Arena beyond the summer when his contract expires
The experienced attacker, 35, has been struggling to get regular first-team action in this campaign due to the stiff competition for places at the Bavarians, and he is unlikely to get more playing time next term following the signing of Lewandowski.
Nevertheless, Pizarro is adamant that the arrival of the Poland international does not affect his Bayern future.
"I am feeling very well at Bayern and would love to stay here," Pizarro was quoted as saying by TZ.
"That Lewandowski is joining Bayern in the summer does not change anything for me. I will have to wait and see how I feel in the next six months or so and then make a decision on my future.
"Lewandowski is a top player and he has already proven his worth. He will do well at Bayern and make us even stronger."
Pizarro's current Bayern deal is due to expire at the end of the season.