The First Minister would become Britain’s most senior politician to appear on the show as she looks to raise her worldwide profile.
Both Gordon Brown and Tony Blair have previously faced off against host Jon Stewart, who is set to leave the show in August, though neither UK politician was Prime Minister at the time.
Ms Sturgeon is travelling across the Atlantic for what is mainly a business oriented trip, with the SNP leader scheduled for meetings at the World Bank, IMF and an address at the Council on Foreign Relations.
Discussions regarding The Daily Show appearance are said to be ongoing with the Scottish Government refusing to confirm or deny the plans.
A spokesperson said: “The programme for the first minister’s visit is still being finalised, but is expected to include a number of media opportunities to help promote Scotland.”