Adam, 26, missed the home defeat to Wigan last Saturday after suffering the injury against QPR three days earlier and fears have been mounting that he may be out for the rest of the season.
However, Dalglish insists that there is still hope for the Scotland international, though the length of his absence will not be confirmed for another two weeks.
"Charlie's another two weeks and then we'll find out a proper diagnosis without people speculating what's wrong,'' Dalglish said.
"Rather than be inaccurate or incorrect or someone making up a story we will wait and see in a couple of weeks how long he's going to be out.''
Adam has plenty of company on the sidelines with Craig Bellamy (calf), midfielder Maxi Rodriguez (illness) and defenders Glen Johnson (calf), Daniel Agger (rib) and Martin Kelly (ankle) all also absent from the Wigan game.
Dalglish, though, said he is hoping to have some better news on the injury front as he prepares to take his side to Newcastle this Sunday, with the Reds looking to avoid a sixth defeat in seven Premier League games.
"We have a very strong squad which has been stretched but so have other people who are in a similar position,'' Dalglish said. "It was stretched at the weekend after three games in seven days but that has gone now.
"The clear week we have gives everyone a chance, if they have bumps and bruises, to get rid of them and it gives the boys another week to get fit. We should get a few back but is only Thursday for a Sunday game.
"Everyone else is progressing, including Lucas Leiva (whose season was ended in November by knee surgery) who will obviously not play but who has done brilliantly in his recuperation.''