The First Minister will say the US constitution is the "supreme example" of setting out a country's "dearest and most enduring principles".
He was due to deliver the lecture at Glasgow Caledonian University's new New York base as Yes campaigners yesterday welcomed another poll showing an increase in support for independence.
The Panelbase survey, for pro-independence website Wings Over Scotland, put support for a Yes vote on 47% and backing for No on 53% when the 14% of undecided voters were excluded.
The findings were in line with other polls which have shown the No campaign's lead shrinking since the start of the year.
In his speech today the First Minister will say: "One of the first and most exciting tasks of an independent Scotland will be to devise a constitution for our new nation. And in doing that we will undoubtedly look for inspiration to the US constitution."
He will also highlight the "fundamental importance" of the Scottish Government's decision to restore free university tuition and argue that an independent Scotland would make a "strong and positive influence on the wider world" through peace keeping or humanitarian work.
In a thinly-veiled attack on UK foreign policy he will say: "You can aspire to be a great nation, without desiring to be a great power. The USA is both.
"But most nations can't be. And they reduce their chance to be a great nation, if they pretend to be a great power."
The speech is part of the States' Tartan Day/Scotland Week celebrations marking the anniversary of the Declaration of Arbroath in 1320 which influenced the US Declaration of Independence. The latest Panelbase survey put the Yes vote on 41%, No on 46% and don't-knows on 14% in rounded figures.
The vote for both sides was up by one point compared with Panelbase's previous poll and, apart from a widely criticised survey last year, marked the highest result so far for the Yes camp.
Blair Jenkins, the chief executive of the pro-independence Yes Scotland campaign, said: "This is a very encouraging poll. What it clearly indicates is that 'Project Fear' is failing and that increasing numbers of people are realising that Yes promises a better future for themselves, their families and for Scotland." But speaking on the BBC's Andrew Marr show, Alistair Darling, head of the rival Better Together campaign, said: "The majority of people in Scotland are against independence.
"I believe we will win this campaign as long as we get our arguments across that we are stronger and better together.
"There is a very strong powerful case for staying in the UK - for jobs, opportunities and the ability to make Scotland a fairer and more just place to live. We have strong bonds of culture, kinship and family. We have a shared history of 300 years. That's a positive argument that we will continue to make."
The poll came amid reports the SNP, though increasingly confident of a shock victory in September's referendum, was preparing to back moves to give Holyrood more powers in the event of a No vote.