It comes after George Osborne warned of "self-defeating" hikes a day after a Treasury colleague said there was a "strong case" for looking at increasing it.
Iain Duncan Smith, the Conservative Work and Pensions Secretary, and Vince Cable, the Liberal Democrat Business Secretary, are said to be pushing for an above-inflation rise of 50p or more to provide "shock value" ahead of the General Election and seize the initiative from Labour.
The Chancellor made clear he wanted to see a rise in the £6.31 an hour minimum wage but not at the expense of jobs.
His comments came as he highlighted the new Employment Allowance, which will allow businesses to claim £2000 a year off their employers' National Insurance contributions.
The move from April 6, has been described as a "cashback on the jobs tax" for every business in the UK.
Asked if a big rise in the minimum wage was on the cards, the Chancellor replied: "Everyone wants to see an increase in the minimum wage; I would like to see an increase in the minimum wage. But it has to be done in a way that doesn't cost jobs, because that would be self-defeating."