Analysts have predicted that the rapper's second collection Pink Friday: Roman Reloaded will knock Madonna's MDNA from the top by Sunday.
Minaj is expected to sell between 200,000 and 225,000 copies of the album during its first week on sale, reports Billboard.
The sales would take Pink Friday: Roman Reloaded to the top of the Billboard 200 and mark the star's second chart-topper after her debut Pink Friday reached the summit in 2011.
Meanwhile, Rascal Flatts' new album Changed is expected to debut with a top three position, while Adele's 21 will also remain towards the top of the chart.
Nicki Minaj is on course to claim her first UK number one album with Pink Friday: Roman Reloaded after the set topped the midweek chart.
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Listen to Nicki Minaj's 'Roman Holiday' below: