Uncertainty has surrounded the size of the cuts since Conservative Finance Minister George Osborne said they would be greater than the 11 billion pounds announced in June's budget.
But Osborne's Cabinet colleague responsible for welfare said later that he did not recognize a four-billion-pound figure for the extra cuts reported in the media.
Alexander told the Scotsman that the government needed to scrutinize welfare payments further. Asked if he recognized the four-billion-pound figure, Alexander said: "I think I wouldn't want to say it was going to be limited to that amount."
Pressed on whether it may be more, he said: "We haven't decided on a number yet." Alexander, a Liberal Democrat, was speaking before the annual conference of the junior coalition party.
Uncertainty arose last week when Osborne told the BBC that detailed welfare cuts to be set out next month "will amount to several billion pounds additional to what I announced in the budget".
The BBC said this would amount four billion pounds but Osborne has not confirmed or denied this figure since.
Conservative Welfare Minister Iain Duncan Smith told legislators he did not recognize the four billion pound figure. Duncan Smith, who is still in talks with the Finance Ministry, said he was opposed to steep cuts that would hit long-term programs to reduce unemployment.
An extra four billion pounds on top of the 11 billion pounds of cuts already announced would together amount to around six percent of the welfare budget.
Cutting the budget deficit, a record in peace-time, was a chief Conservative campaign promise before the election in May. However, the Liberal Democrats opposed many budget cuts until they joined the coalition that ousted the ruling Labour Party.
Liberal Democrat leader and Deputy Prime Minister Nick Clegg defended the change in policy because of an increased risk of spillover from Greece's fiscal crisis in May.
Clegg said in an interview on Saturday that he would try to convince skeptical activists of this at the annual conference.
"I totally understand that some of these people are not happy with what the Lib Dems are doing in coalition with the Conservatives," he told the Independent newspaper.
"The Lib Dems never were and aren't a receptacle for left-wing dissatisfaction with the Labour Party. There is no future for that. There never was."
