Washington's Smithsonian Institution had asked to borrow Chia Chia, to mate it with US-based Ching Ching.
But Mrs Thatcher said pandas were not "happy omens" for politicians.
Cabinet secretary Sir Robert Armstrong wrote: "Lord Zuckerman sees this as a signal demonstration of the special relationship and would be very happy to time the announcement of the loan or the delivery of the panda in any way that the prime minister thought would be most likely to benefit Anglo-American relations.
"He even suggested that the prime minister might like to take the panda in the back of her Concorde, when she goes to Washington next month."
But Mrs Thatcher's private secretary, Clive Whitmore replied: "She has commented that she is not taking a panda with her - 'Pandas and politicians are not happy omens!"'
The file also showed Mrs Thatcher's initial response. On a briefing note about the idea, she had written in blue felt tip pen: "I am not taking a panda with me". To emphasise her point she underlined the word "not" twice and also underlined the word "me".
She then added: "Lord Z knows more about pandas than I do - I am sure he can arrange these things."
The National Archives in Kew, London, holds more than 11 million official documents, many of which have been transferred from government departments and are often opened as public records after 30 years.
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