The midfielder was troubled by a groin problem last season and the club announced last week that he would miss the start of the forthcoming campaign because of an infection that required hospital treatment.
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.
New recruits: Liverpool manager Kenny Dalglish is the man in the middle of (from left) Jordan Henderson, Charlie Adam, Alexander Doni and Stewart Downing
'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.'
While Gerrard will certainly be missed, Dalglish has concentrated on strengthening his midfield in his summer recruitment, with Downing, Henderson and Adam estimated to have cost more than ?40million between them.
The Scot has been impressed with their impact so far, and said: 'Everybody you bring in you hope is going to improve the quality you already have here.
Injury jinx: Gerrard has been battling infection in his troublesome groin
'That's what we're hoping from all of them, just to be themselves and go about their work as well as they did at their previous clubs.
'They're pleased that they've come here and we're delighted to have them.'
The upturn in form towards the end of last season, coupled with Liverpool's financial outlay, means expectations among their supporters will once again be sky high for the new Barclays Premier League season.
Pre-season has been mixed, with the Reds conceding three goals in each of their five games, including defeats against Hull and Galatasaray, but Dalglish is confident things will be different once he fields his full-strength side.
He added: 'It could have been better but we've had a lot of people coming in at various times. Everybody that has been with us has got a reasonable amount of time on the pitch. As we get closer to the Sunderland game we'll pare it down a little bit.'
One player hoping to take advantage of Gerrard's absence is 21-year-old Henderson, who established himself as one of the most promising young English midfielders after coming through the ranks at Sunderland.
Centre stage: Scotland midfielder Adam appears to be settling in fine at Anfield
He said: 'Obviously Steven will be a massive miss but it's a real opportunity for us coming in to stamp our authority on the team and get our chance.'
It will be a doubly emotional experience for Henderson if he does make his debut in the opening match of the season next weekend, with Sunderland the visitors to Anfield.
'I've just got to treat it like a normal game,' he said. 'All my family and friends are Sunderland supporters so I'm sure they'll be wanting Sunderland to win but I'm a Liverpool player now.
'Hopefully it'll be my Premier League debut for Liverpool.'
Adam will also be hoping to stake his claim in central midfield after finally being granted permission to join Liverpool from Blackpool.
Special delivery: Downing will be expected to supply crosses into the box
The Seasiders blocked a move in January as they battled, ultimately unsuccessfully, against relegation, and Adam admitted he did have concerns his chance may have gone.
The Scot said: 'When you're at a club that's fighting relegation you know it's going to be difficult to leave.
'The situation was I wanted to come to a massive club like this. Blackpool made the decision that I couldn't go and I respected that.
'I think the performances I had from January until the end of the season proved I was 110 per cent behind the club.
'I'm just delighted to be here as a Liverpool player. It's time to move on and look forward to the future.'
Downing, believed to be the most expensive recruit at around the ?20m mark, impressed for both Aston Villa and England last season and was also linked with a move to Arsenal this summer.
The winger is hoping a continuation of that form for his new club will see him play more of a role for the national team building up to next year's European Championships.
He said: 'First and foremost I have to do well for Liverpool. I've had more of a chance with England over the past couple of months, which I've really enjoyed, so long may that continue.
'The European Championships is an incentive.'
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