Kane has scored at least 20 goals in the past four Premier League seasons, including netting 23 so far this campaign.
Chiellini said the England international deserved to be compared to Messi, Ronaldo and Neymar – widely regarded as the best three players in the world.
"Kane is now among the elite players in the world. Over the last years, with the goals he has scored, he has been on the level of the best," the Juve defender said ahead of his side's meeting with Tottenham in the Champions League on Tuesday.
"Messi, Ronaldo, Neymar – Kane has been on that level. He is one of those players that is irreplaceable and I am sure that Tottenham will be doing all they can to make sure he stays."
Kane's form has seen the forward linked to the likes of European champions Real Madrid.
Chiellini said no fee would stop the world's biggest clubs from signing a player they wanted.
"It is now a game where you cannot even guess at valuations anymore. There are maybe four or five teams who will pay whatever they need to pay to get the player," he said.
"They are huge sums, but that is the world we now live in — when one of those four or five teams want a player, then they usually get them."