The Scot - who led Liverpool to three league titles in his first managerial stint at Anfield between 1985 and 1991 - feels Manchester United's 1-0 victory over Arsenal last Sunday has put the champions back into contention for the title.
But the 62-year-old believes that with 11 games played in the Premier League this season, Liverpool and Southampton - who sit second and third respectively - must be considered among the contenders to win the league.
"A lot of the focus last weekend inevitably fell on Manchester United’s 1-0 victory over Arsenal," Dalglish wrote in The Daily Mirror.
"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.
"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.
"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."
Despite their impressive starts to the season, Dalglish feels Liverpool and Southampton will only remain with the leading pack if managers Brendan Rodgers and Mauricio Pochettino strengthen their squads in the January transfer window.
"Nobody really considered either of them - especially the Saints - legitimate contenders for a top-four place this season," the Scot continued.
"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.
"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."
