John Healey, a former Labour minister who represents the Wentworth and Dearne constituency in Westminster, will hold a meeting with Mr Gove on Thursday over the Three Valleys Independent Academy proposal.
Last week, the Department for Education gave the company behind the academy approval to develop plans further for a free school in an existing building in Manvers, near Rotherham.
Mr Gove pushed through legislation shortly after the General Election to allow parents, charities and businesses to apply to set up independent or "free" schools to be funded with state money.
At the same time, he scrapped Labour's 55m Building Schools for the Future programme, which would have seen more than 700 secondary schools across Britain improved or rebuilt.
Mr Healey said he had compiled a 14-page report on the requirement for a free school in South Yorkshire and claimed that if allowed, it would have a negative effect on existing schools.
He pointed out that many local schools already had excess places, including Rawmarsh School, where teachers recently went on strike over redundancies announced as a result of falling pupil numbers.
Mr Healey said: "I want Michael Gove to publish hard evidence that this plan is serious. At no point have the people behind it demonstrated the credibility to run a secondary school.
"The Government seems determined to drive these free schools into some areas whether or not there is a strong case for doing so, and never mind the effect on local schools and students.
"I will be challenging Michael Gove on Thursday to publish the proposal for the Three Valleys Academy, which we haven't seen, and the evidence that it is needed, which we haven't seen."
Plans for the Manvers school were originally drawn up by an organisation called NICHE, but the reins have now passed to a charitable company called Three Valleys Independent Academy Trust.
Mr Healey added: "If I had parents queueing up outside my office saying they wanted this school the position may be different, but parents, teachers and headteachers have contacted me with their concerns.
"Everything is being done behind the scenes. This is taxpayers' money we are talking about, it's not something that should be done as a deal in private."
Nobody from the Three Valleys Trust was available for comment yesterday, but in a recent interview with the Yorkshire Post, chairman David Mann said there was "huge interest" from parents.
He added: "Our view is that if the Government is going to make this money available, then we should be bidding for it. This is as good an area as any to spend it in."
Existing independent schools are also looking to exploit the free school policy. One of those considering the move is Batley Grammar School which will ditch its charges of up to 2,949 per term if it is given approval to join the state sector in September.