The paper reproduced that drawing on its website on Tuesday.
At the time, the cartoons drew little initial attention but were later reprinted outside Denmark, provoking outrage among Muslims, most of whom deem any depiction of the prophet as offensive.
Three Danish embassies were attacked and at least 50 people were killed in rioting in the Middle East, Africa and Asia.
Several young Muslims have since been convicted in Denmark of planning bomb attacks, partly in protest at the cartoons.
Lene Espersen, Denmark’s justice minister, said she had been briefed by the PET but could not comment further.
Danish media said Westergaard has been under PET’s protection for several months.
The Islamic Faith Community, a Muslim organisation at the centre of the cartoon controversy, condemned the plot, saying all disagreements should be handled via legal channels.
In a statement, it said: “It does not serve our purpose that people take the law into their own hands. On the contrary.
“We want to appeal to reason in both politicians and the media to not use this miserable example to feed the flames or use it for their own profit. No one in Denmark deserves to live in fear.”
In the 2006 book The Mohammad Crisis, written by Per Bech Thomsen, Westergaard said he did not expect the cartoons to become a global affair.
“The idea was to illustrate that terrorists get their ammunition from the fundamentalist parts of Islam,” Westergaard said.
“It was not aimed at Muslims and Islam in general, but against the part that inspires and uses death and destruction.”
Westergaard told Thomsen he felt misunderstood.
“I was part of the project to strike a blow for freedom of expression and the anger over being threatened because one does one’s work, drowns out the fear,” he said.