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".
The claims put further pressure on Infantino, who is facing calls to resign as FIFA president over the World Cup private investment plan.
The 56-year-old has apologised for "errors" he made in those controversial proposals, but did not step down after receiving the backing of senior executives in a meeting in Morocco on Wednesday.
Infantino joined UEFA in 2000 and became secretary general in 2009, before being appointed FIFA president in 2016.
European teams have threatened to boycott FIFA events despite the plans being aborted, saying certain conditions have not been met.
But Conmebol - the South American confederation - and the Confederation of African Football (Caf) have backed Infantino, as have the football associations of World Cup co-hosts Mexico and tournament runners-up Argentina.
