The Telegraph said Jack Warner, the former vice-president of FIFA, appeared to have been personally paid dollars 1.2 million (pounds 720,000) from a company controlled by a former Qatari official shortly after the controversial decision to award the country the tournament.
Payments totalling almost dollars 750,000 (pounds 450,000) were made to Mr Warner's sons, according to documents seen by the Telegraph. A further dollars 400,000 (pounds 240,000) was paid to one of his employees.
The Telegraph also said a company owned by Mohamed Bin Hammam, the then FIFA executive member for Qatar, appeared to pay dollars 1.2 million (pounds 720,000) to Mr Warner in 2011.
Bin Hammam, who launched an abortive challenge against incumbent FIFA president Sepp Blatter, resigned from his FIFA and Asian Football Confederation posts in 2012, shortly before was banned for life from football administration by the global governing body's ethics committee.
Warner was one of the most experienced members of the executive committee until he stood down in 2011 and served as vice-president of FIFA for 14 years.
He was one of the 22 people who decided to award Russia the 2018 World Cup and Qatar the 2022 tournament.
Six weeks before the December 2010 vote in Zurich that decided the hosts of the 2018 and 2022 World Cups, an official was caught in an undercover investigation agreeing to sell his vote. A second member of the same committee was recorded asking for pounds 1.5 million for a sports academy. Both officials were suspended, meaning that 22 people voted instead of the usual 24.
The decision to give the World Cup to Qatar, a country with little football history, provoked widespread condemnation particularly over health concerns for leading players forced to play in the desert nation's stifling summer heat.
Such was the backlash football chiefs are now considering moving the tournament to the European winter for the first time, even though this could have a severe adverse knock-on effect on some of the sport's major domestic competitions such as the lucrative English Premier League.
There was a particularly bitter reaction to the whole process in England, the birthplace of modern-day football, after the country's bid to stage the 2018 finals garnered a mere two votes and was eliminated in the first ballot.
Giving evidence to a subsequent British parliamentary inquiry, Lord David Triesman, the English bid's former chairman, named Warner as four FIFA executive committee members had asked for business deals and favours when negotiating their support
In June 2011, Trinidad-based Warner resigned from all football posts after he was accused of facilitating bribes to members of the Caribbean football union (CONCACAF) on behalf of Bin Hammam, who was standing against Blatter.
A FIFA ethics committee found there was "compelling" evidence Warner was "an accessory to corruption".
The Telegraph said Warner and his family had declined to comment on their report but a spokesman for Qatar's 2022 World Cup organising committee told the paper: "The 2022 bid committee strictly adhered to FIFA's bidding regulations in compliance with their code of ethics.
"The supreme committee for delivery and legacy and the individuals involved in the 2022 bid committee are unaware of any allegations surrounding business dealings between private individuals."