According to plans being discussed by Buckingham Palace and organisers of the anniversary celebrations, the Queen would present the new charter at Runnymede in Surrey, where King John sealed the original in 1215, The Sunday Times reported.
The presentation would be witnessed by Justin Welby, the Archbishop of Canterbury, senior members of the royal family, the prime minister and the leader of the opposition.
Parliamentary clerks, lawyers and constitutional experts are to be consulted on whether a resolution of the Commons and the Lords is required, the daily said.
"The Queen would be reconfirming the values of Magna Carta in the 21st century," a source was quoted by the daily as saying.
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"That would be freedom under the law, the notion that nobody is above the law, equality and access to justice," the source said.
The plan will be seized on by those who view the anniversary celebrations as a way of reaffirming British values.
David Cameron wants every child to be taught about the "British values" in the charter, which he has described as "the foundation of all our liberties".
The charter is widely known throughout the English speaking world as an important part of the protracted historical process that led to the rule of constitutional law in England and beyond.