The Mail on Sunday reported that Leighton made this a condition of him agreeing last week to stay on as chairman for the next three years.
Leighton is believed to want to offer 31% of Royal Mail to investors, which would raise around £4bn, and give 20% of it to its workers.
The story drew a strong denial from the DTI and opposition from the Communication Workers' Union. CWU general secretary Billy Hayes said the organisation should remain in the public sector.
A Royal Mail spokesman said: "It is a matter for the government and it is our understanding that it is not on its agenda."
Leighton and chief executive Adam Crozier are currently gearing Royal Mail up to face unfettered competition from April 2006, and have managed to turn losses of £1m a day into profits of £1m a day.
The organisation was hit by unofficial strikes last winter after disagreements between workers and management on working practices and pay, but relations have improved since then.
In April 2003, the Institute of Public Policy, a left-wing think tank, advised the government to privatise Royal Mail to allow it to respond faster to competition.
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