Suarez was heralded as a new Anfield hero after arriving during the January transfer window, and playing an integral part in Liverpool late-season resurgence under Dalglish.
And while most players would have been looking to a well-earned break over the summer, Suarez flew off to Argentina to represent Uruguay at the Copa America, where he helped his nation win the title.
Due to his international commitments, Suarez returned back for pre-season training later than most of his team-mates, and it Dalglish initially conceded it might take awhile before the Uruguayan international was back to his best for Liverpool.
However, Suarez has made a mockery of these concerns with his blinding start to the season, having already scored two goals in three league matches.
And while Dalglish reveals he is looking to regularly give his players a break, he admits Suarez does not look in danger of burnout anytime soon.
"He had a break before they [Uruguay] met up for the Copa America and another break before he came back here," Dalglish said, according to The Sun.
"We will just manage the situation. We would love him to play in every game, train in every session but it might not be practical.
"We are not going to make any predictions other than we will look after him, just like every other player.
"And he's on such a high after Uruguay's success that his adrenaline level must be right up there. And that won't run out for Luis - he won't accept that success is finished for him.
"He certainly doesn't look jaded. He has got a high level of fitness, and he thrives on responsibility."
Suarez is already a firm favourite among the Liverpool faithful since his £23million in January, and has shown signs of forging a promising partnership with Andy Carroll up forward for Liverpool.