The Reds have enjoyed a spectacular start to the 2013/14 campaign, dropping just 10 points en route to a second-place standing in the Premier League table.
Just two points separate them from leaders Arsenal, while their offensive and defensive records are as good as anyone in the division.
The challenge now is to build on a bright start and mount a sustained push for a first top flight title in 24 years.
Dalglish, who is now a non-executive director at Anfield, sees no reason why Brendan Rodgers' side - along with another 'surprise package' in the form of Southampton - cannot remain in the mix if they come out of the winter transfer window stronger than they enter it.
He wrote in his Daily Mirror column: "A lot of the focus last weekend inevitably fell on Manchester United's 1-0 victory over Arsenal.
"It was a big win for United and their new manager David Moyes because it put them right back in the frame as title contenders.
"By stopping Arsenal, it also brought a lot of teams into contention again when they must have feared they were slipping out of the race.
"But I thought the teams that fared best were Southampton and Liverpool.
"They are the two sides that have been the surprise packages of the season so far and they appear to be the ones playing with the most freedom.
"They look fresh and eager and I think they are both being helped by the fact they don't have to worry about European football this season.
"Of course, you want to be involved in the Champions League and the Europa League, if you can, but sometimes you can use your absence from those competitions to your advantage.
"We are not yet a third of the way through the season, but we are not far off and it is getting to the point where we have to take the claims of Southampton and Liverpool seriously.
"Nobody really considered either of them - especially the Saints - legitimate contenders for a top-four place this season.
"But they are reaping the benefits of not having to adapt to a new manager, as many of the leading clubs are having to do.
"It has got to the stage now where, if they buy in January, I think both might have a real chance of staying up there.
"We know that the top teams will all strengthen. Manchester United, Arsenal, Chelsea and Manchester City will all buy in the next window.
"So, if they can - if finances allow it - then Liverpool and Southampton need to do the same.
"If they do that, the rewards could be considerable. They have got themselves in position. Now they have to try to seize their opportunity."
Keeping Suarez - who has already netted eight goals this season and has struck up a fearsome SAS strike partnership with Daniel Sturridge - will be crucial to the Liverpool cause, with reports of interest from Real Madrid refusing to go away.
Dalglish added on the Uruguayan frontman: "There will be speculation about Luis Suarez leaving the Reds. There always is. But I don't think he's going anywhere.
"He's thriving in this Liverpool team and everyone at Anfield knows he is crucial to maintaining a challenge."