The group are number one on the iTunes tally and are expected to sell between 160,000 and 180,000 copies of Up All Night in the States, Music Week reports.
The feat would make them the first UK band to enter at the top in America with their debut LP.
Last month, their first single 'What Makes You Beautiful' became the highest-charting debut entry on the tally for a UK act, landing at number 28.
The band are in the midst of an extensive promotional tour of the States, having already performed on The Today Show and due to appear on Saturday Night Live on April 7. They also concluded a ten-date support slot for Big Time Rush last week.
Meanwhile, fellow UK boy band The Wanted are at number four for a second week on the Billboard singles chart with 'Glad You Came'. Their US album is expected to follow later this year.
> Katy Perry congratulates One Direction on US iTunes chart success
Watch One Direction's 'What Makes You Beautiful' music video below: