Alan Shearer's men face Liverpool at Anfield on Sunday sitting in the relegation zone, three points behind Hull in 17th, but Dalglish believes the rest of the run-in will be kind to the team from the North East.
He said: "I think Newcastle will stay up. They have two home games left against Fulham and Middlesbrough. If they win those it will take them to 37 points. Hull also have Bolton and if they win it will take them to 37 as well. I don't see too many points coming for Hull or Newcastle apart from the ones I have mentioned, so then Newcastle would stay up on goal difference."
Steven Gerrard is set to return aid Liverpool's title challenge, after missing four games with a groin injury, with the prospect of leaders Manchester United being six points clear of the Reds if they win at Middlesbrough on Saturday.
He scored twice in the 5-1 win at St James' Park earlier in the season and is looking to create yet another piece of scoring history.
Gerrard's next goal will be his 118th for Liverpool, placing him joint 12th with Ian St John in the club's all-time list.
And Liverpool are just one goal short of recording 300 in the Premier League under manager Rafael Benitez, with their next goal being their 50th in all competitions at Anfield this season.
Just for good measure, Dirk Kuyt is one goal short of equalling his best season's tally for the club.
Dalglish added: "This is a game that both sides have to win, but Liverpool will know exactly where they stand because Manchester United are playing at Middlesbrough on Saturday.
"It seems that Sir Alex Ferguson is going to make a few changes at Middlesbrough, but he does not put out too many bad sides so it doesn't matter who he fields. But if Middlesbrough get a return from the match then Liverpool will really be left with a big game on Sunday."