The Sunday Times claims the Energy Select Committee Chairman Tim Yeo admitted in secret filming that he coached a paying client on how to influence his committee.
Mr Yeo rigorously denies any wrongdoing.
The paper also says he discussed a fee of £7,000 a day to act as a "paid advocate" for a energy company.
Mr Yeo says he did not accept the offer because he realised it was not permitted under House of Commons rules.
He now plans to refer himself to the Parliamentary Standards Committee.
More top news
Chancellor George Osborne has announced a £500m investment for the Faslane naval base in Scotland, home of the UK's nuclear deterrent.
Five-times major winner Maria Sharapova has pulled out of the US Open tennis championships due to a leg injury.
Police are hunting for a mother who has disappeared with her 10-week-old baby.