The England midfielder, who will be 32 in May, signed an extension to his existing deal, but is already looking to go beyond his current contract.
Dalglish admits fitness will play a big part - Gerrard's last year has been dogged by a groin problem which required surgery and then an ankle infection - but sees no reason why the talismanic skipper cannot emulate Manchester United's Ryan Giggs.
"You have to wait and see how they get through injuries," said the Scot. "Giggs is 38, isn't he? That's seven years down the line - that's a long time to predict - but if he's fit there's no reason why not.
"I've not got a crystal ball. I'm just delighted he's done what he's done and we have got him here."
Dalglish has always been considered Liverpool's greatest player but the Reds boss believes Gerrard must now come into the reckoning, saying:
"I wouldn't disagree he has certainly made a huge contribution to the club but he wouldn't be far away from being mentioned as the best player."
Gerrard will be involved in Saturday's clash with Stoke, alongside Jose Enrique.
Enrique was left out for tactical reasons in the Carling Cup semi-final first leg win over Manchester City but is likely to return.
Midfielder Jay Spearing sustained a minor hamstring injury in midweek and that is likely to allow Charlie Adam to regain his place.
Stoke boss Tony Pulis is hoping the encounter will not see the referee come under the spotlight again like in the previous two meetings between the sides this season.
Reds manager Kenny Dalglish was unhappy with several decisions made by match official Mark Clattenburg during his team's 1-0 league defeat at the Britannia Stadium in September.
Pulis' feelings were then similar after the Potters were beaten 2-1 at the same venue by the Merseysiders in the Carling Cup the following month.
The Welshman's criticism of referee Lee Probert on that occasion led to him being warned as to his future conduct by the Football Association and handed a ?10,000 fine, which he subsequently appealed against and is still waiting to hear further news about.
There has been more controversy involving Liverpool this week after a two-footed tackle by Reds defender Glen Johnson on Manchester City's Joleon Lescott went unpunished, and Pulis does not want such issues to be at the fore once more in the game tomorrow.
"I think with every game you go into, you hope it is won and lost by the players," Pulis said. "You hope that referees don't affect it in terms of decisions that change a game of football.
"That is all you hope for, but they are human beings and they will make mistakes like every player and manager does."
Pulis has concerns over a number of players.
Defenders Jonathan Woodgate, Marc Wilson and Ryan Shotton are all nursing what Pulis describes as "niggles" and will be assessed.
Andy Wilkinson could return at the back having overcome his recent knee injury, while the likes of goalkeeper Thomas Sorensen, winger Matthew Etherington and striker Peter Crouch are set to be restored to the team after they were rested for last weekend's FA Cup victory at Gillingham.
Source: PA