The Spanish attacking midfielder suffered ligament damage in his left knee in City's Premier League clash with Newcastle United in October.
Manager Manuel Pellegrini said Silva's return to the park had been pushed back, with the 28-year-old still suffering soreness in the problem area.
The Chilean boss said he could not put a timeline on the World Cup winner's return.
"We don't know [when Silva will be available], because David still feels some pain in his knee, so he's not able to kick the ball," Pellegrini said on Friday.
"We'll see if next week he can be ready at the end of the week.
"It will depend on the way he improves in the next few days."
Pellegrini refuted the suggestion Silva had suffered a setback with his injury, and was hopeful of an improved prognosis within the week.
"In the last day, he still feels a little pain but not very, very hard [pain] so I hold out [hope] in the next week we have good news about David," he added.
Silva's confirmed absence against Bayern - already unsurpassable atop Group E - is a further blow for Pellegrini, who will be without suspended midfielders Yaya Toure and Fernandinho for the crucial clash.
City sit bottom of the group on two points, two shy of second-placed Roma.
