Either Smith, a 12-year-old British opera singer, or Muir, a singing Scottish plumber, could be crowned the winner of the competition series in Saturday night's finale, the Times of London said.
Smith and Muir will compete against the winner and runner-up of Friday night's semifinals -- as well as six other previously determined finalists -- for the title and a $200,000 cash prize.
"When you enter a competition like this, you pray to find someone like you. You are literally one in a million," judge Simon Cowell, usually known for his sharp criticism, told Smith after she performed the Sarah McLachlan ballad, "Angel," Thursday. "Anyone hearing you for the first time tonight should remember this occasion because you have the most incredible future ahead of you. You're super talented."
The Times said Muir secured his place in the finals by performing Paolo Nutini's song "Last Request."
Judge Piers Morgan told Muir the performance was reminiscent of last season's winner.
"You've come on stage tonight and I felt a bit of a Paul Potts moment," Morgan said.