Clarke was brought in by Dalglish on a short-term deal to work alongside him until the end of the season.
The former West Ham and Chelsea coach has made a big impact alongside the Reds boss since they took charge at Anfield.
With Dalglish looking likely to be handed a long-term deal, Clarke is hopeful their partnership will continue.
"Every manager I've worked with - you pick up good qualities from all of them and so far, in a short space of time, I've seen a lot of great qualities from Kenny," he said.
"I hope to continue the work into the future. Anyone watching us play right now can see the spirit is high, the confidence is good and the performances have been decent. Now we need to continue it.
"If you are working well as a group and working well day in, day out in training - you can see they're taking that onto the pitch right now. If you've got that togetherness it goes a long way in any team sport - especially football."
Liverpool have blooded the likes of youngsters Jack Robinson and John Flanagan in recent games, and Clarke has paid tribute to Dalglish for his approach with them.
"Before Jack went on Kenny was making a joke and trying to relax him going onto the pitch," he said.
"Obviously it's a very nerve-racking moment for a young player and Kenny was trying to take the edge out of the situation. It was the same with John.
"When you've got someone as experienced as Kenny who says the right words at the right time, it can only help."