"The consequences are not yet clear," the newspaper's correspondents said.
"Whether the waking up process was stopped because of the infection is not known."
Schumacher's manager Sabine Kehm said: "We do not comment on speculation."
Professor Heinzpeter Moecke, of a Hamburg hospital, told Bild: "Pneumonia is generally a serious and dangerous disease, because the body is supplied with less oxygen and is weaker."
He said comatose patients sometimes contract pneumonia because ventilation prevents coughing.
"A healthy person coughs or swallows several times per minute, usually without noticing it. This protects the lungs," said Moecke.
Schumacher's former Ferrari teammate Felipe Massa told reporters in Sao Paulo this week that he recently visited his friend in the Grenoble hospital.
"I went to see him on a day when there was nobody from the press there.
"I stayed by his side for a long time," said Massa. "It was good to be there.
"It just looked like he was sleeping, like any of us sleeps.
"I'm really hopeful everything will be ok and that he will wake up and recover fully," said the Williams driver.
Massa said he is receiving daily updates from the Schumacher circle about the great German's condition.