He acknowledged discussing a fee of £30,000 with the undercover reporters but said: "I am not aware of having offered to do anything for these people that was outside the rules."
He went on to say that any arrangement would have been based on a written contract and would have involved advising them on how to get amendments to legislation - but he would have been acting strictly as an adviser and consultant.
A third peer, Lord Taylor of Blackburn, said two people approached him claiming to work for a lobbying firm and looking for help with a bill they wanted amending.
He said they suggested paying him £5,000 to £10,000 a month as an adviser but he never said he would accept, no contract was signed and no money changed hands.
Asked about his alleged suggestion that the rules could be "bent", he said: "'Bent' to me means you will try to persuade the bureaucracy of the House to change them."
Former Labour whip Lord Snape indicated that he could help amend a bill for a fee of up to £24,000 a year, the Sunday Times alleged.
The paper said Lord Snape issued a statement "saying that he had made it clear to the reporters that he was unable to 'initiate or amend any legislation on behalf of an individual or a company'.
"However, he said he did think the reporters' proposed exemption might be 'beneficial' and undertook to 'investigate' further," the paper said.
'Named and shamed'
Lady Royall told BBC News an investigation would be launched "if or when a complaint is made" and it would be carried out by the House of Lords Committee for Privileges, whose members include Lord Irvine of Lairg and Baroness Manningham-Buller.
Speaking on the BBC's Andrew Marr show, Lady Royall said she did not feel "comfortable" reading about the allegations, and if they were true, it would be a "very grim picture".
If anyone needed any reminder of how threadbare and weak the creditability of the way we do politics has become, they just need to look at today's headlines
Lib Dem leader Nick Clegg
"Clearly, it looks very serious but I'm concerned everybody's side of the story should be heard. We don't have trial by media in this country," she said.
"For the moment, these are allegations and I want to ensure they are properly investigated."
Lady Royall went on to say that if it emerged the peers had broken the rules, they would be "named and shamed" but they could not be thrown out of the House of Lords.
Liberal Democrat leader Nick Clegg told Andrew Marr that people would be very angry reading about the "allegations of total corruption".
Lord Truscott has denied offering to put down amendments for cash
"If anyone needed any reminder of how threadbare and weak the creditability of the way we do politics has become, they just need to look at today's headlines," he said.
Shadow business secretary Ken Clarke told the BBC One programme the Commissioner for Standards had to carry out an independent inquiry.
"If the allegations are true, I'm afraid this one is very serious - to take money to try to alter legislation for the benefit of the people paying you a fee... I think some people would call that corruption," he said.
Sir Christopher Kelly, chairman of the Committee on Standards in Public Life, said he would await the outcome of the House of Lords investigation to see whether it was "an area" the watchdog needed to look at further.
BBC political correspondent Iain Watson said trying to influence Parliamentary legislation was outside the House of Lords code of conduct, but peers not paid a salary can offer general advice to private firms as consultants.
"That may be where there's a bit of a grey area, where people can quite honestly say 'I haven't broken any rules'," he said.
The Sunday Times said its reporters had posed as lobbyists acting for a foreign client, who was setting up a chain of shops in the UK and wanted an exemption from the Business Rates Supplements Bill.
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