The qualification has already been adopted by around 200 private schools in the UK, even though it is not recognised in Government league tables.
Some state schools, such as the London Oratory, are also keen to offer the IGCSE , which is sat by more than 100,000 candidates overseas. But, because it is not recognised by the Qualifications and Curriculum Authority, no funding has been available for them to do so.
Lord Adonis said: "The IGCSE is a reputable qualification which some schools in this country clearly regard as beneficial to their students." He told the House of Lords that a QCA report on the qualification was to be published and that the Government would look at the results of its consultation with "an open mind".
Sir Cyril Taylor, chairman of the specialist schools and academy trust, said he expected the trust would recommend the qualification to the country's 2,379 specialist schools. "It would offer more choice and rigour," he said. "There is lots still to be worked out such as equivalency. But my instinct is that it is likely to be popular with specialist schools."
Lord Adonis's statement was in marked contrast to the stance taken by ministers only last month that the IGCSE could not be adopted in state schools because it did not fulfil the requirements of the national curriculum.
It also follows the news, revealed by The TES last month, that the ministers are considering giving all state pupils an entitlement to study for the international baccalaureate.
Cambridge Assessment, which with Edexcel offers the IGCSE, said it welcomed the consultation. The qualification has been available internationally since 1988, when the O-level was abolished and is recognised worldwide.