Sources close to the programme said the star's representatives had asked for a fee of around £2.5 million.
They said: "We just can't afford to pay those big salaries."
The BBC has been criticised in the past for paying large salaries to its stars and recently unveiled plans to axe 2,000 jobs as it tries to make savings of 20%, worth £670 million a year by 2016/17.
Chart star Jessie J has already signed up to the show, which is being seen as the BBC's answer to The X Factor.
In the show, contestants will win through purely on the strength of their voices rather than how they look, with "blind" auditions.
Kylie's sister Dannii spent four years as a judge on The X Factor and has been tipped to appear in the next series of Britain's Got Talent.
The US version of The Voice featured Christina Aguilera and Cee Lo Green as coaches.
Other names linked to the show, which is expected to be screened on Saturday evenings, include Lenny Kravitz and Tom Jones.