He made the statement in an email to BBC staff following a report in the Evening Standard today, which claimed insiders at the corporation are expecting 14,000 jobs to be axed following the BBC's review into the cost-saving demands of the 10-year Royal Charter.
Thompson said: "Inevitably, staff numbers are one of the issues we are looking at in the context of Value for Money but the idea that anyone anywhere in the BBC is seriously suggesting making half the BBC redundant is simply preposterous."
He urged staff to ignore speculation in the media until recommendations from the review had been made.
According to reports in The Observer in October, senior BBC management estimate 6,000 staff will be made redundant in order to meet the cost-saving demands of the Royal Charter.
Trade unions also expect up to 6,000 jobs to go when the results of the corporation's review are announced, the bulk of these from entertainment programme-making departments, which is inevitable if the BBC independent production quota is increased from 25% to 50%.
A BBC spokesman said: "Any reports about the review at this stage are merely speculative. The results will not be announced until December."
There are currently four ongoing reviews at the BBC, which will determine the exact nature of the job cuts.
The first concerns the future of the BBC's commercial arm, BBC Worldwide, which it is considering selling part of. The division incorporates the BBC's books, DVD and magazine businesses.
The second is looking at content supply systems, which regulates who makes programmes.
The third review is considering whether the BBC should move more of its services out of London to cut high rent and rate costs. The final review is examining whether the BBC is "value for money".
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