Britain's biggest banks are in talks about collectively reducing the amount they will award in new year bonuses.
BBC business editor Robert Peston said negotiations about the "thorny" issue were taking place under the umbrella of the British Bankers Association.
One participant suggested that total bonuses could be cut from £7bn to £4bn, but accepted such a figure would still attract criticism from politicians.
A senior banker stressed there was no guarantee of a "workable agreement".
"We are talking to each other about making some kind of joint statement about bonuses that would demonstrate that we are reducing the amount we are allocating to remuneration this year," the banker added.
With the rest of the economy undergoing belt-tightening measures and banks still being accused of not lending money to small businesses, the bonus issue will be monitored closely when it crops up in the new year.
Business Secretary Vince Cable has been critical of "outrageously large" bonuses in the past.
Responding to news that bankers may voluntarily reduce their bonus payments he said: "Banks have been significant recipients of public generosity in the past few years."
"In return, it is quite reasonable to have high expectations of the way they conduct business, and that they are encouraged to show restraint in how they reward themselves during this difficult time," he added.
One participant in the private talks told our correspondent: "What's the most we could achieve? Right now the expectation is that banks in the City will pay out around £7bn in bonuses."
"Maybe we can cut that to £4bn. But although that would be a huge reduction, £4bn is still a big number - and we'll still face attacks," the banker added.
Our correspondent says the talks themselves may be counter-productive as the banks could be seen to be colluding on a competitive issue and could therefore be prosecuted by the Office of Fair Trading.
"One of the great paradoxes about all of this is that ministers would love us to agree to cut bonuses, but they're powerless to stop us being prosecuted under competition law," one banker said.
However, British Bankers' Association insisted that there were no negotiations under way.
In a written statement it added: "It is no secret the major UK banks ... have sought for some time to get an international agreement on bonuses."
The BBA believes that the UK has the toughest regime for bankers of any G20 country but is, "well aware of the public view [on bonuses] and will take this into account when bonuses are decided."
The statement went on to say: "Right now, speculation about the size and the issue of bonuses is just that - speculation."
Any cap on bonuses could lead to top banking talent relocating to other financial centres where there are fewer concerns about big pay, says our correspondent.
British banks are said to be irked that Wall Street is resistant to the idea of a mutual agreement on restricting bonuses.
"There's no chance that the big US investment banks will follow our example, which means that business and good people could leave London for New York or elsewhere, if we're seen to be paying less than the market rate," one banker said.
The total size of the bonus pool on Wall Street for 2010 performance is expected to be about $20bn (£12.4bn), or about 80% greater than the expected London bonus pool.
Tax income reduced
The estimated figure for City bonuses this year is already sharply down from the £11.6bn awarded at the height of the financial boom in 2007.
If this figure falls further to £4bn, as suggested, this would mean a drastic reduction in tax revenue that goes to the government.
The Centre for Economics and Business Research (CEBR) estimates that the tax authorities will lose about £1.8bn in revenue.
Douglas McWilliams, chief executive of the CEBR, said that the City financed a major part of public spending in successful years.
"Seeing the banks attempting to drive a coach and horse through competition law to pay their employees below the market norm should cause sensible people to get worried," he said.