Gianni Infantino's alleged lover was given a severance payment over the affair by Uefa while he was its general secretary, according to a Daily Telegraph investigation, external.
A spokesman for the now Fifa president was reported to have told the paper Infantino "strongly denies these categorically untrue allegations".
Uefa, for whom Infantino was general secretary from 2009 to 2016, issued a statement confirming "a departure payment was made to the individual in question".
The allegations come as Infantino fights for his future as Fifa president following his aborted plans to sell off stakes in the World Cup to private investors.
BBC Sport has contacted Fifa and Infantino for comment.
The Telegraph reported that Uefa paid a six-figure sum to the woman, who had an alleged relationship with Infantino, who is married, during his time at European football's governing body.
"Fifa president Gianni Infantino strongly denies these allegations, and they are categorically untrue. Any insinuation of inappropriate conduct or violation of statutes or regulations is defamatory," a Fifa spokesman told the Telegraph.
"No employee at Uefa and Fifa has ever raised a complaint regarding Mr Infantino's behaviour because there never was an incident where he was involved."
Uefa confirmed a payment was made to the woman in question and that it covered the fees for her to complete an MBA course at a local business school.
It said all payments were in line with regulations at the time, but those regulations have since been tightened and "reflect those found in a modern, high-profile organisation".
A spokesman for the now Fifa president was reported to have told the paper Infantino "strongly denies these categorically untrue allegations".
Uefa, for whom Infantino was general secretary from 2009 to 2016, issued a statement confirming "a departure payment was made to the individual in question".
The allegations come as Infantino fights for his future as Fifa president following his aborted plans to sell off stakes in the World Cup to private investors.
BBC Sport has contacted Fifa and Infantino for comment.
The Telegraph reported that Uefa paid a six-figure sum to the woman, who had an alleged relationship with Infantino, who is married, during his time at European football's governing body.
"Fifa president Gianni Infantino strongly denies these allegations, and they are categorically untrue. Any insinuation of inappropriate conduct or violation of statutes or regulations is defamatory," a Fifa spokesman told the Telegraph.
"No employee at Uefa and Fifa has ever raised a complaint regarding Mr Infantino's behaviour because there never was an incident where he was involved."
Uefa confirmed a payment was made to the woman in question and that it covered the fees for her to complete an MBA course at a local business school.
It said all payments were in line with regulations at the time, but those regulations have since been tightened and "reflect those found in a modern, high-profile organisation".
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