The 'Starships' singer was first rumoured to be in final negotiations with American Idol on Monday (August 20), but the deal was apparently stalled later in the week.
A source close to the negotiations told The Hollywood Reporter that Minaj's Pepsi sponsorship was problematic given American Idol's endorsement deal with Coca-Cola. Those issues have apparently now been resolved.
Minaj is expected to earn $8 million (£5.06m) to become an American Idol judge, although she will probably receive more money for wardrobe, makeup and hair costs.
The insider claimed that Minaj is likely to formally agree to the deal as early as this weekend.
Keith Urban - who recently confirmed in the Australian media that he is speaking with American Idol bosses - is apparently close to a deal worth $3-4 million (£1.9-2.5m) to join Minaj and Mariah Carey on the panel.
Carey formally joined American Idol in July and is apparently earning $17 million (£11 million) for the upcoming season.
Nick Jonas, Kanye West, Snoop Dogg and Diddy are said to have also been in talks for American Idol.
American Idol returns to Fox in 2013.
Watch Nicki Minaj's 'Starships' music video below: