The Chief Secretary to the Treasury will say £100 of the savings will come within the first year of another coalition government. He will outline the manifesto policy to delegates at the party's spring conference in York.
The LibDems faced humiliation on the eve of the event when it was beaten by the Bus Pass Elvis Party in a council by-election in England.
Meanwhile, Business Secretary Vince Cable hit out against another party which has recently overtaken the LibDems at the polls, Ukip, suggesting they were helping the cause of Scottish independence. He said: "Let me say this to Ukip and so-called Eurosceptics in the Tory party. You are also putting at risk the union of the UK. How on Earth do you expect to persuade the Scots to ignore the siren voices of nationalism and separatism when you indulge in British nationalism and Euro-separatism?"
The tax cut will come in the form of a raise in the personal tax threshold - the amount below which workers pay no tax - to £12,500. A rise to £10,000 was included in the LibDem manifesto at the last election.
David Cameron said he would like to implement the raise but suggested it would cost too much money.
In recent months, the Coalition parties have battled to claim credit for the policy, which has lifted many low-paid workers out of tax altogether.
Mr Alexander's announcements confirms hints senior LibDems have been dropping for months. But the Tories are also thought to be considering a similar pledge - potentially leaving two main Westminster parties making the same offer to voters.
Mr Alexander will say: "We will fight the next election with our own ideas, our own policies, our own values - no one else's.
"And I can tell you that a top priority in any negotiation will be our aspiration to raise the personal allowance dramatically again in the next Parliament.
"To raise it to £12,500. Conference, that would be a further tax cut for working people of £500. At our first fiscal event in the next Parliament, we would deliver another tax cut of at least £100."
He will add that, in total, two terms of a LibDem government would have, by 2020, delivered a tax cut for working people of £1200. The personal allowance is due to rise to £10,000 next month. The party is pushing for another rise, to £10,500, to be announced in the Budget the week after next.
He will also re-open the feud on the issue by telling delegates the tax cut was "resisted by the Conservatives".