According to The Mirror, the Britain's Got Talent runner-up's performance will coincide with the release of her debut album I Dreamed A Dream.
A show insider said: "It makes perfect sense and will create a big buzz.
"There are two shows to fill on Saturday and Sunday nights now, so they're also planning guest appearances from previous winners and runners-up as well as celebrity guests."
Earlier this year, presenter Dermot O'Leary said that Boyle would sing a duet with a mystery performer when she appears on the show.
Last year's winner Alexandra Burke and former Take That star Robbie Williams will reportedly perform on the first live programmes of the series.
It has been suggested that the second week will feature live music from Whitney Houston and show judge Cheryl Cole.