Goldie Hawn's charity runs schools in the US and Canada
The Tories are in talks with foreign educational groups - including one run by Hollywood actress Goldie Hawn - to set up state schools in England.
Shadow Children's Secretary Michael Gove says he is talking to the French government and a Swedish schools chain.
And he told The Sunday Times his team had also spoken to Ms Hawn's charity, which promotes Buddhist values.
Schools Minister Vernon Coaker questioned how the plan could be funded without "cuts to existing schools".
The Tories want parents, charities and companies to take over failing schools or set up new ones if they win power.
Mr Gove told BBC One's Andrew Marr show he wanted to give state schools the same "freedom" as fee-paying schools to set their own curriculums, which he claimed would boost the chances of pupils from poorer backgrounds reaching top universities.
"What we want to do, for example, is to allow organisations like a Swedish company, the International English School, the chance to come here to teach the sort of rigorous academic curriculum which too many students, particularly students in poorer parts of the country, are denied."
He said an independent body would scrutinise anyone that wants to set up a school "to make sure that extremist organisations, or people who have a dark agenda, are prevented from doing so. The other thing that we will make sure is that schools are inspected rigorously".
And he stressed that he did not want to see schools teaching "creationism", which rejects scientific explanations for life on earth in favour of religious beliefs.
"To my mind you cannot have a school which teaches creationism and one thing that we will make absolutely clear is that you cannot have schools which are set up, which teach people things which are clearly at variance with what we know to be scientific fact."
But if schools are properly inspected and regulated "anyone who teaches in a way which undermines our democratic values can be brought to light, challenged and if necessary, closed down".
He said "hundreds" of parents and groups of teachers had been in touch with the Conservatives to express an interest in the plans.
In an interview with The Sunday Times, Mr Gove said he wanted Sweden's International English School to take over failing schools if the Conservatives win the election and his team had held talks with the French government about establishing state schools based on the Lycée Français in South Kensington, London.
The Lycée Français is a private institution which provides a French education for French expatriates and British parents who want their children to grow up bilingual.
"Under our plans you could have UK citizens sending their children to the Lycée at no cost because it would be fully integrated into the state sector," he told the Sunday Times.
Mr Gove said his team had also recently met actress Goldie Hawn, whose Hawn Foundation charity runs schools in America and Canada and is said to be keen to open a school in the UK.
The Hawn Foundation teaches the Buddhist technique of Mindfulness training, which emphasises social and emotional progress over academic testing and the use of simple breathing exercises to boost learning power.
Mr Gove told The Sunday Times he could not see any serious barrier to her setting up a school within the English state system.
"We are going to have another meeting to discuss how she might be able to help and influence education here."
'Extra running costs'
He added: "Some parents would want a rigorous traditional academic education for their children with desks neatly marshalled and traditional football. Others will want something that is more flexible, more imaginative."
But Schools Minister Vernon Coaker said: "For the first time, Michael Gove has admitted that the Swedish schools he wants to open with 220,000 additional surplus places would involve extra running costs."
He challenged Mr Gove to "explain to parents where the estimated £1.8bn costs of these new surplus places would come from without big cuts to existing schools".
Mr Coaker said: "Michael Gove's claim that these reforms raised standards has been undermined in the last week by the Swedish Ofsted and international studies which have shown a big drop in school standards in Sweden.
"Now his claim that there would be no extra costs has been blown apart by his own admission he would need to find money from elsewhere to fund them."