The 22-year-old, whose £35million price tag is a record for a British player, has not had chance to turn out for his new club as he has been sidelined with a thigh injury. His last game was for Newcastle on December 28.
"Whether he will be involved on Sunday, I'm sure Fergie (Sir Alex Ferguson) would love to know, but we don't know yet," said Dalglish, who celebrates his 60th birthday on Friday.
The Reds boss has always insisted he would be patient, but with the striker taking part in full training sessions this week, there is a chance he could be in the squad to face Liverpool's arch-rivals at Anfield.
Dalglish was giving nothing away, however, at his pre-match press conference.
He said: "His training is always progressing but he has not yet progressed to a game yet."
"We have said all along we have been delighted with his progress and what he has done.
"There have not been anything which he has done which has not been encouraging."
And after he and Carroll were pictured at a concert in Liverpool last week Dalglish joked: "He might not even be a substitute - he might be going to see Boyzone."
Source: PA