Armstrong has been out since suffering a calf injury before the 3-0 win at Anderlecht before the international break, while Brown came off injured in Belgium with a hamstring issue.
Both players missed Scotland's World Cup qualifiers with Slovakia and Slovenia as a result of their woes and the Celtic boss does not expect them to be involved on Saturday when the Hoops host Dundee at Parkhead.
The Northern Irishman does, however, believe that Brown and Armstrong will be fighting fit when the Bhoys travel to the Allianz Arena on Wednesday.
He told STV: "Scott Brown and Stuart Armstrong are very unlikely to be involved on Saturday but all three [including Jozo Simunovic] should train and hopefully be ready for Bayern Munich.
"[Brown and Armstrong] are great. They've come through very, very well.
"They'll join the squad tomorrow for training and maybe Saturday is too soon for them but certainly Bayern Munich should be fine."
Having both players invovled would be a huge boost for Celtic.
As it stands it seems like a massive ask to even come away from Bavaria with a point, but that mission is certainly that bit more possible with the pair than without them.