"We have a couple of knocks with Rhys Webb and Justin Tipuric," Edwards told reporters on Monday.
"We will wait until the last minute until we name the team on Thursday. We will give them as much time as possible before making an educated decision.
"They will have to take some part in training before Thursday to put their hands up for selection."
Wales, who are looking to end a run of 12 defeats in a row to Australia, are running out of options at flanker with Sam Warburton, Ellis Jenkins and James Davies also on the sidelines with injury while Thomas Young has not been included in the squad.
Edwards said Wales would face a real challenge from Australia, who arrive on the back of victories over world champions New Zealand and 2019 World Cup hosts Japan.
"We all know what an unbelievable attacking threat Australia are, averaging 33 points a game," he added.
"They are perennially a top-four ranked team, their attack is pretty prolific and they have a multitude of excellent backs."
(Reporting by Hardik Vyas in Bengaluru; Editing by Peter Rutherford)
