The 'Price Tag' popstar is apparently unable to take part because of extensive tour commitments which would clash with filming, while Jones has allegedly pulled out after taking advice from his manager and son Mark.
However, will.i.am and Danny O'Donoghue will be back when the show returns in 2013, according to The Mirror.
The newspaper report contradicts claims from The Sun, which said that Jones would be back for a third series, as long as he likes the other coaches.
Leanne Mitchell, who was mentored by Sir Tom Jones, won the first series of The Voice earlier this year.
The Voice's first run was a hit for the BBC, securing the channel's highest launch ratings for an entertainment show in a decade. It also beat Britain's Got Talent during head-to-head battles in the schedules.