At the moment millions of staff on the statutory payment receive £6.31 an hour.
But the UK Government has indicated that the recent upturn in the economy could allow an above-inflation rise.
Such a move would be worth more than £1200 a year to employees who work full-time.
Critics argue that the minimum wage has not risen enough in real terms in recent years to keep pace with the rising cost of living.
Ministers have asked the official body in charge of the rate to consider an increase.
But evidence submitted by the UK Government suggests that a rise would not affect jobs or hit businesses.
Mr Osborne said: "I think Britain can afford a higher minimum wage.
"I think we have worked hard to get to this point and we can start to enjoy the fruits of all that hard work.
"The exact figure has to be set by the Low Pay Commission, which talks to business, talks to other bodies in our economy.
"But, if for example, the minimum wage had kept price with inflation it would be £7 by 2015/16."
He added: "I think we can see an above-inflation increase in the minimum wage and do it in a way that actually supports our economy precisely because the economy is recovering and many, many jobs are being created.
"Of course we have got to make the exact calculation of what the rate should be. That's for the Low Pay Commission. But, when I look at the British economy I see the British economy expanding, I see jobs being created, I see the prospect of future jobs being created as well and I think Britain can afford a higher minimum wage."
The Chancellor's comments came just days after he warned against a "self-defeating" increase in the minimum wage rate to a level that would cost jobs.
Labour accused the Chancellor of "flailing" under pressure. Chris Leslie, the party's shadow chief secretary to the Treasury, said: "The Tories cannot hide from the fact that working people on average £1600 a year worse off since they came to office. "We need action now to earn our way to higher living standards and tackle the cost-of-living crisis."
l Scottish independence would lead to a "race to the bottom" on the minimum wage, Harriet Harman, the deputy Labour leader, has predicted.
Ahead of a visit to the Cowdenbeath Holyrood by-election today, Ms Harman said: "A question-mark is raised over whether there would be a kind of race to the bottom (after independence). Of course, there would be once you have a break. That's why we didn't want to set a separate minimum wage for Scotland, a separate minimum wage for Wales, the south east or Cornwall.
"(When Labour introduced the mimimum wage) we asked - what is a decent minimum? "It disproportionately benefited people in Scotland."