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, told Sky News that he had done nothing wrong.
"I have never, never in my career in the Lords or in local government, done anything that I am ashamed of in any way," he said.
Former Labour whip Lord Snape indicated he could help amend a bill for a fee of up to £24,000 a year, the newspaper said.
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.
A spokesman for the Committee on Lords' Interests said an investigation would be launched if a complaint was received, which is expected on Monday.
It would be the first major inquiry by the committee since it was set up a few months ago.
Lady Royall told BBC News that she would also continue to pursue her own inquiries by speaking to the four peers concerned more fully.
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".
Lord Truscott has denied offering to put down amendments for cash
"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.
Shadow business secretary Ken Clarke said 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 told Andrew Marr.
Lord Strathclyde, the shadow leader of the Lords, said there should be "a swift investigation".
"The rules are clear," he said. "There are no grey areas. Paid advocacy is banned and should remain so."
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.
This firm was said to be setting up a chain of shops in the UK and wanting an exemption from the Business Rates Supplements Bill.
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