According to latest updates,Captain Steven Gerrard is recovering faster than predicted from the groin infection.
He was admitted to hospital last week due to infection and he it is said that he will miss the start of the forthcoming campaign because of infection.
At a press conference to introduce summer signings Stewart Downing, Charlie Adam, Jordan Henderson and Alexander Doni, Dalglish said: "Steven won't be too far away. All the tests that have come back are far better than what was anticipated so we're delighted with that for him.
"He's had some really positive news and we'll just wait for the progress to continue. But the date that has been mentioned hasn't been changed."