With the Scot's famous No.7 shirt now adorned by Suarez, comparisons between the pair were inevitable, but Dalglish wants to allow the Uruguayan the opportunity to be his own man.
Dalglish was quizzed about the similarities between himself and the Reds striker following Liverpool's 2-1 win over Wolves, in which Suarez netted his eighth goal for the Merseyside club.
And the Liverpool boss was quick to relieve the pressure on Suarez to follow in his footsteps.
"I think everyone has their own identity and it undermines the boy if you compare him with anyone else," said Dalglish.
"He is Luis Suarez. He is a fantastic player and it is not fair to compare him with others who have been here before.
"Does he benefit from working with me? I don't know - I don't speak espanol! I don't know where he gets his ideas from but he is full of them and he certainly knows how to play.
"The fans take to him because he is so genuine and 100 per cent committed. The crowd love players like that. He has his own ideas and he is full of them. He is just a fantastic player."