A Daily Telegraph investigation claims 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 from 2009 to 2016.
The story has ramped up pressure on Infantino's position, with several football federations already calling for him to go, after abandoning a failed plan to sell off stakes in the World Cup to private investors.
A FIFA spokesperson has confirmed Infantino strongly denies the story and any involvement in it.
"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.
"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 did confirm a payment was made to the woman in question which covered 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 to "reflect those found in a modern, high-profile organisation".