Treasury select committee member David Ruffley is calling for the department of business, innovation and skills to be abolished.
Business secretary Vince Cable currently runs the department but Ruffley says it is unproductive and the money saved can be re-invested
BIS has a wide remit covering policy areas such as consumer issues, regulation, economic development and employment matters.
Ruffley believes further spending cuts should be made to fund major building projects as capital spending has been cut by 48 per cent since 2010.
He told BBC Radio 4: “Some of us think we should close down the department of culture, media and sport and BIS and close down non-productive parts of Government activity.
“If you take both departments you would save £3bn to £4bn for starters. By 2015, under the current austerity programme, we are only going back to spending rates in this country of 2008.
“We are only reducing expenditure by 3.5 per cent so there is room for more public expenditure cuts and without slackening austerity we would be able to get on with some capital expenditure projects.”
Ruffley’s calls come on the back of Mayor of London Boris Johnson calling on the Government to stop “pussyfooting around” and boost growth.