The Reds boss is hoping the England forward will be fit in time to face his old club, but concedes that he will not be selected if he does not fully recover in time
Alan Pardew's side will travel to play the Reds at Anfield on Sunday, with the £35 million forward in a race to be fit in time to play against his former employers.
Now Dalglish has admitted that he is willing to give the 22-year-old a chance to return in time for the weekend game, suggesting he will give the England forward right up until the last moment to prove his fitness.
"It's only Thursday and there's a few days to go yet," Dalglish told reporters. "I don't think nature knows it is Newcastle so if he's not fit, he's not fit.
"For Andy it is a poignant game but if he's not fit we can't do anything about that."
Dalglish also hailed his opposite number for steadying the ship and guiding his side to a mid-table position with Newcastle currently 11th in the Premier League.
"I think they've had a very good season," he said. "They are newly promoted and had a change of manager. There was a lot of furore about it but he's [Pardew has] gone on and done very well.
"In the January transfer window he lost Andy who came here and they didn't have an opportunity to replace him because they ran out of time. So I think they can be well satisfied with what they have done this season."