The Specialist Schools Trust lists the discredited energy firm as one of the sponsors of the UK's 1,986 specialist schools.
The Texas-based company, which was valued at more than pound;40 billion at its height, went bankrupt in December 2001 after massive hidden losses were uncovered.
Ralph Hodge, former head of the firm in the UK, said sponsorship and donations were the best way of getting access to ministers.
The trust refused to name which school had received money from Enron, saying it was confidential and would not comment about whether the school was embarrassed about the link now.
But specialist schools have other controversial sponsors including several arms companies, such as BAE Systems, Westland Helicopters and Vickers, which makes the Challenger tank.
Mr Clarke said: "There are no companies in principle which we would say cannot give sponsorship if they have a commitment to education and schooling.
"We don't want to go down the route of sorting out sheep and goats, as to who's OK and who isn't."
He said the basic rule was whether accepting a donation was legal, and whether companies obeyed the law.
Enron did not fall foul of this rule, despite eventually being at the centre of one of the world's greatest financial scandals.
Sir Cyril Taylor, chairman of the trust, said that companies could not have ulterior motives in offering cash to schools.
He said: "Sponsorship has to be genuine. It cannot be on condition of purchasing a company's products."
But the trust does list "advantageous tax concessions" and "favourable publicity" among the reasons why firms might choose to donate. Sponsors are also allowed to appoint governors and are encouraged to offer pupils work placements and careers advice.
Chris Keates, acting general secretary of the National Association of Schoolmasters Union of Women Teachers, said the reputation of British education could be harmed if schools were linked to disreputable companies.
She said: "If the Education Secretary is going to go down the route of getting involved in private companies, there ought to be at least some ethical policy about the kind of company that is allowed.
"The issue is what damage can be done to the credibility of an establishment if these companies with a history of dubious practices, or perhaps financial irregularities, are the sponsor.
"I don't think you can just wash your hands of what these companies get up to."
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