Speaking to the BBC's Today programme, he said the Scottish Parliament would discuss the request to hold another Scottish independence referendum next week and he was confident a vote to ask for one would be passed.
In Edinburgh, Nicola Sturgeon said she would be "up for" a discussion with May about the timing of a new independence referendum.
It followed Prime Minister Theresa May rejecting calls for a second independence vote before Brexit.
Mrs May told delegates: "Our Party believes heart and soul in our United Kingdom of Great Britain and Northern Ireland".
While Sturgeon has pledged to hold another referendum, former Respect MP and host of RT's Sputnik program George Galloway has cast doubt on Scotland's chances of becoming a member of the European Union once independent, claiming the country is "far from being in love with the European Union in the way the SNP like to think".
With the European Union (Notification of Withdrawal) Bill finally receiving Royal Assent after going through both houses of Parliament, the Prime Minister, Theresa May, has finally been given the power, as expressed by the people of the United Kingdom in the referendum on June 23 a year ago, to invoke Article 50 and start the process of the UK leaving the European Union.
Labour said it would be "entirely unacceptable" to hold such a vote as senior SNP figures, including the First Minister, declined to rule out holding a vote without the consent of the UK Government. "That would be a democratic outrage", Robertson said, as aired by the Sky News TV channel. The government has achieved its ambition of passing a "straightforward" two-line bill that is confined to the question of whether ministers can trigger Article 50 and start the formal Brexit process.
Scotland's First Minister Nicola Sturgeon's plans for a second independence referendum were rejected by May.
A third time, Mr Swinney said: 'I think the Prime Minister would be ill-advised to stand in the way of the democratic wishes of the people of Scotland, as expressed democratically in the elected Parliament'. "The coming negotiations with the European Union will be vital for everyone in the United Kingdom". Areas like Paisley have long supported Scottish bids for independence. May has said she will do so later this month.
In response to May's remarks, Sturgeon tweeted that the prime minister must lack confidence in her own timetable if she thinks Brexit negotiations will not be laid out by autumn next year.
But EU negotiators warn it could take two years just to settle the divorce terms, and agreeing on a new relationship for the United Kingdom and the EU could take years longer.