The fact that the odds are moving in favor of Milan is a bad sign (if you are going to bet on Liverpool), usually such a movement (even a small one) means that the bookmakers have "changed" their mind. I don't think Liverpool will aim for a 100% result in the Champions League group stage, as the Premier League remains their priority. It seems to me that even a coefficient of 2.0 here does not compensate for the risk.
Liverpool are still sharp and strong despite the fact that their focus might be on the premier league, I think they would still give their best towards the winning of the champions league which they are very capable of and I know with the way they started their season they can do something to surprise most of the big teams in champions league like real Madrid who have been struggling of lately.
If I remember correctly, bookmakers rate Liverpool as 5-7 title contenders. Yes, luck may smile on them (if Real is eliminated before a personal meeting with Liverpool), but still, the strategy for the season is built around the national championship, since the Champions League is random. In any case, the group stage of the Champions League is not the stage where clubs play at full strength or show their cards.