The Reds manager is leaving at the end of the season, as he looks for a new adventure after a sabbatical from the game.
Dalglish does have concerns that signing both a new manager and new sporting director in one summer will prove challenging.
When Jurgen Klopp goes everyone will be disappointed," Dalglish told William Hill.
"He is obviously doing what he feels is best for him and everybody associated with the club is eternally grateful for what he has done. It is up to whoever gets in to follow him.
It is very negative to say, 'how can you follow Klopp?'. Whoever takes over from him just needs to be themselves. They'll already have 90 per cent of the ingredients for success at their hands so if they don't want to come in and give it a good go then they'll have made the wrong decision.
If they believe in themselves and trust what they have at their disposal, I think it is a great job to take on.
You can't think about trying to emulate Jurgen Klopp, you have to be yourself. I don't know where they'll go with the new manager but they won't get somebody like Klopp.
The relationship he has with the fans is so important and if the next guy can build the same relationship, then he's off to a great start. I'd like to see the new manager be somebody who knows what Liverpool is all about."