Talks on trying to find agreement on new reforms of the House of Lords are starting between the political parties.
Reform for Lords, pictured here in robes for the Queen's Speech
Tony Blair has indicated he has changed his mind on the issue and no longer wants a fully appointed second chamber.
Ministers deny the issue is being raised now to provide a "smokescreen" for the claims of "cash for peerages".
Meanwhile, a Commons inquiry into the claims has been delayed at the request of Scotland Yard so as not to prejudice any possible police action.
The last reforms of the Lords happened in 1999.
Ninety-two hereditary peers were allowed to keep their places in the Lords in that shake-up. Since then attempts to complete the reforms have foundered because of a failure to find consensus.
Lord Chancellor Lord Falconer is conducting the new negotiations on reform.
It is understood that four options will be drawn up for a vote in the House of Commons, with the preferred choice then put forward.
Lord Falconer told BBC Radio 4's Today programme: "Let's see if we can make progress. I think there is a strong feeling and it's been there for some time that we should try to address the issue."
He promised a free vote on the composition of the Lords before the end of the year, even if there was no consensus between the parties.
He said he had raised the issue before the controversy about the Lords Appointments' Commission blocking four Labour donors from getting peerages.
"We were saying it not as a smokescreen but because it is a very important issue," he said.
Lord Falconer said he believed there should be a "substantial elected element" in the Lords but would not put a figure on how big it should be.
Currently, all peers are either appointed or have inherited their titles.
Ex-Conservative chancellor Ken Clarke, head of the Conservatives' democracy task force, said he thought the majority of MPs would back a 70% elected House of Lords in a free vote.
The "scandal" over Labour loans had brought such changes much nearer, said Mr Clarke, who also pushed for more state funding of political parties.
"Some urgent reform is needed on all these fronts if we are to have any chance of restoring the faith of the ordinary, sensible member of the public in the democratic system of this country," he argued.
Lord Strathclyde, the Tory leader in the Lords, said there was some confusion about whether there was the political will to see through reforms.
And he said there was not much point in looking at the reforms unless the House of Lords was made stronger.
Lord McNally, the Lib Dem Lords leader, said it was entirely possible to give the second chamber powers which allowed it to be "uppity" while leaving MPs with the final say over legislation.
On Monday evening, it was announced MPs had agreed to postpone questioning Chai Patel and Sir David Garrard - two of the Labour donors who were blocked for peerages - scheduled for Tuesday.
That followed a meeting between Deputy Assistant Commissioner John Yates, who is leading the police inquiry, and Tony Wright, chairman of the Commons public administration committee.
Mr Wright said Mr Yates was concerned to make sure no evidence heard by the committee would have "any impact at all on any proceedings they might want to bring".
"Just to avoid that, we are going to pause until things are clearer," he added.