The 33-year-old does not fear the competition for places at the Bundesliga giants, and would welcome the arrival of another attacker to the Allianz Arena
The Bavarians have already strengthened their attack with the additions of the Peru international and Mario Mandzukic, but the likes of Ivica Olic and Nils Petersen said farewell to the German giants this summer.
And Pizarro believes it would not hurt to add some more depth to the front line.
"I think it would be a good thing if another striker was brought in. A long season awaits and unexpected things can always happen," he stated to TZ.
"It is important to have enough options in every position in order to compensate if something happens."
The former Werder Bremen star went on to say that he does not fear the stiff competition for places at the Allianz Arena.
"I am sure that I will get plenty of first-team action. We all have more than enough quality."
Pizarro, 33, previously played for Bayern from 2001 until 2007.