The former was absent for Thursday night’s Carabao Cup defeat at Manchester City due to injury and the latter was forced off with a hamstring complaint shortly before half-time.
Both will be sidelined for the Reds’ forthcoming fixtures, which see Klopp’s men travel to Aston Villa on Boxing Day and then host Leicester City on December 30.
Trent Alexander-Arnold could be back in contention for the trip to Villa Park after illness, however, and Alex Oxlade-Chamberlain and Virgil van Dijk are fine ahead of that contest.
Asked for a squad update at his pre-Villa press conference on Friday, the manager said: “Millie didn’t get better since then – he will be out for a couple of games. Same for Bobby.
“Bobby, it’s like this, he is already on the better side of it, even when it is only a few days ago, but it’s not a major thing, so we will look day by day with him.
“Ox is fine, Ox was ill, like Trent, some of the staff as well. That’s why we have to be careful in the moment, absolutely, like everybody, I think it’s going around.
“That makes planning really difficult for the next game because we were 100 per cent clear what we want to do against City and then you have to change in the last second pretty much, that’s not cool but it’s the situation and that might happen against Aston Villa as well so we need to be flexible, stay flexible.
“Apart from that, Virg trained now obviously completely normal so will be there. Trent hopefully will be better; he was not part of the full session but of parts, let’s see how that develops until tomorrow. That’s it.”
Klopp also confirmed Ibrahima Konate is set to return to training with the Reds on December 27 after reaching the World Cup final with France.