The club were in free-fall last season under ex-boss Roy Hodgson, but the return of King Kenny immediately halted the slide.
Liverpool finished the season in fine fashion and there are real expectations the club can once again challenge for honours this term.
Dalglish has further strengthened this summer with the arrivals of Jordan Henderson and Charlie Adam.
The legendary Scot has called on his troops to worry about their own game and he is not concerning himself with whatever else is happening around the league.
"We've got a challenge from everyone in the Premier League, it's not Spurs and Manchester City," he told Sky Sports News. "We've got a challenge to ourselves as well. We're only concerning ourselves with what we do.
"What we do is going to get us a lot further than if we start worrying about everyone else that we'll play against.
"We're good enough to put on a good performance against any team. We'll try our best to do that.
"The most important thing for us is how other teams are looking at Liverpool. Other teams see Liverpool as a bigger threat."
Adam is the club's newest signing after joining from Blackpool and he is hoping they hit the ground running next month.
"I'm hopefully here to help the guys," commented Adam. "The way we finished last year, if we can take it into this year we'll have a good season."