The Reds skipper has not featured for the Reds since their 3-1 victory over arch-rivals Manchester United on March 6.
A niggling groin problem has laid him low since then, with the problem eventually requiring an operation.
Gerrard is, however, well on the road to recovery and Dalglish is hoping the England international will be back in contention by the time the Reds get their 2011/12 campaign under way against Sunderland.
He told the club's official website: "We start back Monday so we'll see how everybody is then.
"Everything that has been done has been very positive for Steven so we are just hoping for the best for him.
"He deserves a bit of luck on the injury front.
"We won't put him under any undue pressure. All we'll say is that everything has been fantastic so far."
Dalglish has been relatively quiet in the transfer market so far this summer, with Jordan Henderson the only arrival at Anfield.
The Reds are working hard, though, to bring further fresh faces on board and keep their key men out of the clutches of a Premier League rival.
Dalglish added: "I wouldn't mention anyone as a target for us.
"We are obviously trying to bring people in and people are trying to take players from us.
"We are not going to speculate and be disrespectful and talk about other people at other clubs.
"Every manager I've seen interviewed on television has said exactly the same thing. That's the way it should be."