The Peruvian has been used only sparingly since returning for a second stint at Bayern this season, starting only three matches in the Bundesliga and three in the Champions League.
Bayern tend to field one out-and-out striker and, despite being 10th in the all-time Bundesliga scoring list with 164 goals, the 33-year-old is behind Mario Mandzukic and Mario Gomez in the pecking order.
Although coach Jupp Heynckes did not name his team for Tuesday's first leg, it is highly unlikely Pizarro will start despite his efforts in Saturday's 9-2 win.
Heynckes admitted it was a strange situation but said Pizarro was paying the price for joining a club where strength in depth is paramount.
"It's obviously a bit unusual when a player scores four goals in game to then be discussing whether he will be playing in the next game," Heynckes, himself the Bundesliga's third all-time top scorer with 220 goals, told reporters.
"My coach never left me out of the team but we didn't have so many alternatives at the time," he added.
"When a player signs a contract for Bayern Munich he must know there is no guarantee that he will play in each game.
"Obviously, on the one hand, it is not so easy, neither for the coach nor the players, but a club like Bayern must have alternatives and options, to be able to challenge for titles at national and international level."
"That is how it is and we have to accept it."
"We have three centre-forwards, we four absolutely top-class players for the wide attacking positions, and I can only pick three of them at a time."
Bayern have reached two of the last Champions League finals and lost them both and Heynckes suggested that they may have been short of alternatives on the substitutes bench when they were beaten on penalties by Chelsea last season.
"Maybe that is what we lacked in the Champions League final last summer, and that's why the transfer policy for this season was so important," he said.
Bayern have been in dominant form in the Bundesliga this season and, with a 20-point lead over Borussia Dortmund, need only two more from six games.
They have won 23 out of 27 games, scored 78 goals and conceded just 13.
To some extent, their dominance has made a mockery of the Bundesliga's claim to be Europe's most competitive league and Heynckes admitted that they Champions League was a huge step up.
"We must forget about Saturday's match," said Heynckes, whose team scraped through on away goals against Arsenal after losing 2-0 at home in the second let of their round of 16 tie.
"The Champions League is another competition, it's a different standard. This is not just an everyday league. It will be a completely different game."