US tycoon Mr Gates was married and about 55 when he met the Russian bridge player, Mila Antonova, in around 2010 when she was in her 20s.
Wall Street financier Epstein met her three years later before funding her studies at a software coding school.
Convicted sex offender Epstein emailed Mr Gates in 2017 and asked to be reimbursed for the cost of the course, according to the Wall Street Journal.
It followed Epstein failing to convince Mr Gates to participate in a charitable fund.
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