The Reds boss gave a positive update on the England international midfielder, who was ruled out of Saturday's goalless draw against the Swans at Anfield on Saturday and is set for another fortnight on the sdielines.
Dalglish said: "He's fine. Everything been checked and the figures are hugely encouraging and well on his way to recovery."
Meanwhile the Scot backed his Liverpool players to return to winning ways in the near future after they were again held on home soil.
The Reds are unbeaten at Anfield but have now dropped eight points and sit in sixth spot in the table going into the international break.
However, after watching Swans goalkeeper Michel Vorm produce two excellent late saves to deny Luis Suarez and Glen Johnson, Dalglish backed the side to come good.
He said: "We just need to keep working on it and keep getting in there. But we haven't got in there as often as we have done in the past games. The problems there are problems we can solve ourselves.
"We have to look at ourselves and expect better performances than what we produced there."
Dalglish added: "Anything that we were good at, we didn't do too much of, passing and moving, we didn't do too much of that.
"The keeper was tested a few times and usually we are missing the target. That's 11 times we have hit the post or bar this season.
"If we had scored early on it might have changed the way the game went but we never scored so it is hypothetical.
"No-one has ever in the history of football deliberately missed a chance."