The senior Conservative backbench MP Nicholas Winterton has written to Mr Smith arguing that the bid, which is being backed by Mr Murdoch's UK holding company, News International, is "contrary to the national interest".
He has been joined by Baroness Wharton, a cross-bench peer, who has written to Mr Smith telling him that it would be "quite wrong" to allow Mr Murdoch, who already controls four national newspapers and holds a large share in British Sky Broadcasting, to extend his domination into the radio sector.
Mr Winterton, who is Chairman of the Commons All-Party Media Group, also questions the suitability of Mr MacKenzie to run the radio station.
"The prospect of a 'dumbing down' of Talk Radio's output with the radio equivalent of topless darts, news bunnies, and bouncing dwarves fills me with despair," he writes, referring to the features Mr MacKenzie introduced while he was chief executive of L!VE TV, the cable television station owned by Mirror Group.
Mr Winterton intends to raise the issue with Mr Smith and Margarett Beckett, the President of the Board of Trade, in the House of Commons on Tuesday.
He has tabled questions which ask whether the Department of Trade and Industry has any plans to prevent the further expansion into British broadcasting by News International, and whether the competition authorities could intervene in the bid.
Mr Winterton also intends to ask Mr Smith what steps he is taking to promote "plurality and diversity of ownership within the UK media industries".
Earlier this week Mr MacKenzie resigned as the deputy chief executive of Mirror Group to lead a bid for Talk. He is being supported by News International, which under current media ownership rules is allowed to take a 20 per cent stake in the broadcaster. He has also secured the backing of Media Ventures International, the investment group which has a 35 per cent stake in the station.
Mr Murdoch is believed to have wanted to lure Mr MacKenzie from The Mirror, where he had begun to stabilise the troubled tabloid's circulation and threaten the pre-eminent position of the Sun.
However Talk's managing director, Paul Robinson, is leading a management team planning to mount a rival bid for the station, which has been put up for sale by its majority shareholder, the Luxembourg-based media group CLT-UFA. He is expected to name his financial backers next week. Earlier this week, he questioned Mr MacKenzie's ability to run a radio station.
Talk Radio has been in dire financial difficulties ever since its launch. The station soon abandoned a downmarket "shock jock" approach in favour of a more sophisticated format in an attempt to win more listeners. However, it remains hamstrung by the pounds 3.5m annual cash bid it submitted to win the licence. The station is believed to have lost close to pounds 10m last year.
Nevertheless, experts believe Talk will fetch a price of up to pounds 15m, partly because its licence can be renegotiated in two years' time, but also because it has a guaranteed berth on the national digital radio multiplex, applications for which are due in later this month.
This worries Mr Winterton, who argues that a successful bid by Mr MacKenzie would "fly in the face of Government policy objectives by giving Murdoch companies not only control of one of only three such independent national radio stations, but also guaranteed access to digital capacity and potential control of a digital radio multiplex".