The show, which will be launched by the BBC next year, sees celebrity coaches turn their backs on performers as they sing, judging contestants solely on their voice. It has been a hit in the US, where Christina Aguilera, Cee Lo Green, Adam Levine and Blake Shelton mentor the singers.
Williams joining the UK version could see him on a rival show to Take That bandmate Gary Barlow, who is replacing Simon Cowell on this year's X Factor.
An insider told The Sun: "They still have a healthy rivalry and this would kick in if they were on opposing shows.
"Robbie would be great, particularly with his rivalry with Gary."
Adele is also allegedly in the frame to become a judge. Producers of The Voice are apparently pushing ahead with plans to launch the show following rumours that The X Factor is in crisis.
Dannii Minogue is also said to be in talks to join the show following her exit from The X Factor last week.