The singer impressed with her guest judge stint during the show's London auditions, according to The Sun.
Scherzinger, who was axed from the US version of the show after the first series, has allegedly been offered £500,000 to fill the final spot on the panel in the UK.
A source said: "We are talking to Nicole about taking on the job full-time. She is the only person in the frame.
"It's now down to money and whether she can commit to the show, which takes up most of the rest of the year.
"She has given us positive signs. But no-one is counting their chickens after what happened with Dannii Minogue."
The issue of who will complete this year's panel has been the subject of speculation since Kelly Rowland confirmed in April that she will not be returning.
Dannii Minogue was recently tipped for a comeback but reportedly rejected a £1 million offer.
Geri Halliwell was also said to be in the running to become a permanent judge but failed to impress during her guest stint in Liverpool.
