"Which way are they heading?," asked Kicker sports magazine on its front page on Monday, with "alarm for the rascals" the headline of the story.
The Bild daily said: "Super Bayern without Poldi and Schweini."
Schweinsteiger and Podolski, both 22, achieved pop star status in Germany in recent years and helped the national team to third place at the home World Cup in 2006.
But both players came back down to earth with a bang last season, despite Podolski joining Schweinsteiger at Germany's top club. Neither player lived up to expectations and both have also been plagued by ailments in recent months.
Munich, for their part, have invested like never before, with Frenchman Franck Ribery brought in for a league record 25 million euros (34.5 million dollars) to take Schweinsteiger's regular midfield position.
Podolski, who scored just four goals during the last campaign, is confronted with Italy forward Luca Toni and Germany striker Miroslav Klose.
Schweinsteiger and Podolski have admitted they were not at their best last season, but the recent health problems are an additional setback in the important pre-season training.
"They couldn't take part in the preparation in a proper way, that is a certain problem," said general manager Uli Hoeness.
Coach Ottmar Hitzfeld was quoted as saying by Bild that Toni and Klose are the first-choice forwards, but Schweinsteiger and Podolski will get their chance to play as well in a season where Munich aim for a league, cup and UEFA Cup treble.
"I will play if I perform well," insisted Schweinsteiger. Podolski said in reference to Toni and Klose: "I can play football as well, no one should write me off."
But Goalkeeper and captain Oliver Kahn said that both must make a bigger effort this season.
"Bayern is a difficult club for young players, they are confronted with unique stars from all over Europe," he said.
Kahn suggested that the hype may have done both harm: "There was a time after the World Cup when I had to bring a few players down to earth.
"The biggest danger is the moment when you think that everything is great, and when everyone says that you are great. In this moment you can't relax, you must in fact work harder."
But with the pre-season league cup just around the corner, the first round of cup action on the first weekend of August and the Bundesliga kickoff on August 10, time may be too short to convince Hitzfeld that they should be starters.
"Season start for super Bayern. Poldi and Schweine are witnessing it live from the best seats in the house - the substitutes' bench," said Bild.//dpa