The England striker suffered a toe injury in the 1-1 first-leg draw, causing him to miss Saturday's 4-0 triumph at Newcastle United, but returned to training on Tuesday.
With Robin van Persie already ruled out after picking up a knee injury in the UEFA Champions League round-of-16 second-leg clash against Olympiacos, United are eager for 17-goal forward Rooney to play his part at the Allianz Arena as they seek a last-four berth.
"We'll do everything we can (to get him on the pitch)," Moyes said. "He's happy to take an injection to play."
United had been widely tipped to struggle against Bayern in last week's meeting at Old Trafford, but Nemanja Vidic's headed goal threatened to condemn the defending European champions to a rare loss.
However, Bastian Schweinsteiger levelled matters - and was later dismissed - meaning that United will have to score in Germany in order to progress.
Moyes knows his men will be up against it, but backed them to perform under pressure.
"I expect us to play better and I believe we can," he added. "To get through, we will have to.
"We'll need a good performance from everybody. We can't have any passengers."
