Mr Alexander addressed the currency issue in a live STV debate this evening ahead of the independence referendum on September 18.
It featured two teams of three representatives from the Yes and No camps, with each side nominating one person to go head to head on different issues.
Mr Alexander faced Deputy First Minister Nicola Sturgeon to debate the economy and addressed the question of the currency.
Mr Alexander, for Better Together, said that a currency union would leave Scotland with fewer powers.
He said: "The difficulty with the argument that the sovereign will of the Scottish people is a currency union is that the sovereign will applies here in Scotland.
"It can't bind what would be the sovereign will of a separate country after independence. That would be the rest of the United Kingdom so in that sense if Scotland makes its choice, I hope it doesn't, but if we make this choice to be independent on September 18, what then are the realistic choices?
"I don't believe a currency union is in Scotland's interests, that's why I continue to say I don't think a currency union makes sense. It's less powers not more powers here in Scotland."
Last week Professor Joseph Stiglitz, a Nobel Prize winner who was chairman of former US president Bill Clinton's council of economic advisers, said a currency union between an independent Scotland and the rest of the UK could work, and dismissed the refusal of the main Westminster parties to agree to such a deal as "bluffs".
Responding to Mr Alexander tonight Ms Sturgeon said: "It was Bill Clinton's senior economic adviser who said last week the Westminster position was 'a bluff'.
"I do think we're seeing the No campaign's bluff called on this issue.
"To believe that Westminster would engage in what the principal of Glasgow University described as 'economic vandalism' would be to believe that they would cut off their nose to spite their face, to put transaction costs on their businesses, to deny themselves the value of our exports and to let an independent Scotland start debt free.
"I don't think they'll do that."
Later Elaine C Smith, for Yes, highlighted the "appalling" life expectancy of men in the east end of Glasgow and said that independence could address poverty.
She said: "I became a grandmother 14 weeks ago.
"A statistic in the Glasgow Herald shocked me. We didn't know whether it was going to be a boy or a girl that my daughter was having.
"The statistic said one male child in every four born in Glasgow this year will not live until they're 65.
"This is not in Dickens' time, this is 2014. I live in the east end of Glasgow - 58 years of age is the life expectancy of men there.
"That is appalling, and for a lot of people we've looked at politicians who no longer seem to be putting people first and poverty at the top of the agenda.
"And that for me is what Yes can start to deliver."
Labour MSP Kezie Dugdale said that health and social care is already devolved to the Scottish Parliament and called for a "national conversation" about the issues.
She said: "I spent some time in Finland earlier this year, and one of things I learned over there is that people are now planning their government and all their public policy on the basis that one in four people in Finland will live to 100.
"That's the ambition they have got for their country there.
"To be honest, we are not really tackling those issues in Scotland.
"We know we've got an ageing population, but we're not talking about how we're going to deal with that.
"Everything to do with health and social care is already devolved to the Scottish Parliament, and do you know what we are faced with? Fifteen minute care visits.
"Some people only get 15 minutes a day with somebody in their house who gets less than the living wage to be there.
"This is only going to be a bigger problem going into the future.
"We need to have a national conversation about how we fund it and what our priorities are, because everything about the system needs to change.
"It's got nothing to do with constitutional politics. It's about what happens in the Scottish Parliament with the powers that we have over health."