MPs may receive a pay rise of about £10,000 a year amid reports that the Independent Parliamentary Standards Authority (Ipsa) has decided that their salaries are lagging behind civil service pay.

John Bercow, the Commons Speaker, is understood to be sympathetic to a pay rise after saying that MPs are paid an "ordinary" amount of money.

MPs are paid £65,738 a year, a figure that was frozen in 2011 for 2012-13. The leaders of the main parties have resisted pay increases on the grounds that it would be wrong for MPs' salaries to increase while public sector workers are experiencing a pay freeze.

But the Speaker is reported to have complained that David Cameron, Ed Miliband and Nick Clegg have not been "terribly clever or brave" to resist pay increases. Bercow is understood to have pointed out that the three party leaders have all been supported by private family wealth, according to the Sunday Times.

The main party leaders will have to decide how to respond to the findings of the report, which is due to be published next month. They will all be braced for hostile headlines if they accept what will be seen as a dramatic increase in pay.

A survey released by Ipsa in January found that MPs believed on average they should be paid £86,000 a year. Some thought they should be paid £100,000.

The watchdog has been heavily criticised by MPs who believe it shows no sympathy for the demands of maintaining offices in their constituency and Westminster when assessing expenses claims. The body is expected to justify any pay rise by saying that perks, such as higher pension contributions by parliament, have been reduced.

An Ipsa spokesman told the Sunday Times: "There is no recommendation yet, there are no proposals yet. We are working on that. We are going to do this in a very public and proper way with consultation. We will be consulting before the end of June and at that point we will be asking the public what they think of the proposal."