In a statement, the QAF added it had "no knowledge or involvement" of the money allegedly paid out by Oryx Qatar Sport Investments to Papa Massata Diack's Pamodzi Sports Consulting company.
The allegations were made earlier this month in French newspaper Le Monde.
"With regards to Le Monde's article regarding wire transfers from OryxQatar Sport Investments to Pamodzi Sports Consulting, the QAF can confirm that they have no relationship with Oryx Qatar Sport Investments and no knowledge or involvement of the wire transfers to the named party or individual," said the federation in Sunday's statement.
"The QAF upholds the highest standards of ethics and we followed the IAAF's rules at every stage of our 2017 and 2019 bids to host the IAAF World Championships in Athletics.
"We are very disappointed to be named in these allegations.
"In response, legal action is being considered and will be taken if such false allegations continue to be made against the QAF."
It had been alleged by Le Monde that two money transfers were made on October 13 and November 7, 2011.
The payments -- which totalled around 2.5 million euros at the time -- came just a few weeks after Qatar had announced it would bid to host the 2017 World Athletics Championships.
Le Monde said it had seen receipts showing the payments had been made.
The 2017 championships were eventually awarded to London.
Last month the IAAF said it would not investigate bribery claims againstQatar after finding no more than "rumours"" surrounding bidding for the 2017 world championships.
Papa Massata Diack was banned for life from athletics earlier this year.
Lamine Diack, who headed the IAAF from 1999 to 2015, has been charged by French police on suspicion he accepted bribes to cover up doping cases in Russia.
Qatar though was later successful in bidding for the 2019 championships.
The World Athletics Championships in Doha will be held in the Khalifa International Stadium, which will also be used as a venue during the 2022 football World Cup.
FIFA's controversial decision to award Qatar football's biggest tournament is the subject of an ongoing investigation by the Swiss Attorney General, who is examining allegations of corruption in the 2022 bidding process.
