The Inverness MP and Chief Secretary said he was eager to have a live discussion with Mr Salmond ahead of the referendum in a head-to-head in the Highland capital.
Prime Minister David Cameron has already rejected a TV debate with the Scottish leader, claiming it was a matter for Scots.
The First Minister’s office claimed Lib-Dem MP Mr Alexander was acting as a human shield for the Conservatives in Scotland.
A spokesman said: “The First Minister will happily debate with members of the UK Government but by starting at the very top and working his way down.
“Of course, he’ll have to go quite far down before he gets to Danny Alexander.”
Mr Alexander said: “He (Mr Salmond) wants a debate with the UK Government. I am the most senior member who would have a vote on this.
“I hope he would accept the challenge. There is a lot to debate. I would be happy to consider a debate in any form.
“The question of whether we become independent or not is the most important question that most of us will be asked at the ballot box in our lifetime.”
Mr Alexander said Mr Salmond should be willing to step up to make his arguments.