If passed, the series of amendments to the bill put forward by former Conservative chief whip David Maclean would mean that both the Commons and Lords would not be required to release information as stipulated in the act.
But Liberal Democrat MP Norman Baker is attempting to block the bid and has accused the government of trying to unfairly limit freedom of information.
He claims arguments that such a move was necessary in order to protect correspondence between MPs and constituents were unjustified.
"If somebody produces in the public domain information about a third party – in this case an MP's constituent – that is an offence under the Data Protection Act, so there is no question that this already exists as a means for protecting constituents," Mr Baker told the Today programme.
Mr Baker insisted: "This is about exempting MPs from scrutiny in the House of Commons on how for example we get our expenses, how much the House of Commons spends on refurbishment, on what our policy is for example on sourcing food and drink for the House of Commons refreshment department.
"It is about covering up, and it shows that the freedom of information culture which we hoped was becoming established in this country is not in the bloodstream yet."
Mr Baker said that the government had "watered down" the white paper on freedom of information.
"Freedom of information is essential in a modern democratic society," he added.
"I thought we had won that battle. Secrecy only serves to protect the corrupt and the incompetent and I don't think we should be protecting either."
MPs debate the private members bill in the Commons today but a prolonged discussion in the House could prevent it being passed.
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