The BBC reported that the money, sent on behalf of South Africa, was intended to be used for a football development programme in the Caribbean.
Mr Warner, 72, has been indicted by the FBI in the US on corruption charges, but denies all allegations of wrongdoing, as has the South African Football Association (Safa).
The BBC reported that three transactions in 2008, on 4 January 4, 1 February and 10 March totalling $10m were transfered from Fifa accounts to Concacaf, governing football in North and Central America and the Caribbean, controlled by Mr Warner.
JTA Supermarkets, a chain in Trinidad, received $4,860,000 between January 2008 and March 2009. US prosecutors allege the money was mostly then paid to Mr Warner in local currency.
Another $360,000 was withdrawn by people with connections to Mr Warner, said the BBC, who passed the information to Trinidad and Tobago’s sports minister Brent Sancho.
Mr Sancho said: “He [Mr Warner] must face justice, he must answer all of these questions. Justice has to be served.
“He will have to be held to account, with this investigation, he will have to answer for his actions.”
Safa has denied claims from former Fifa executive committee member Chuck Blazer that it issued bribes to win the vote to host the 2010 World Cup.
Mr Blazer has said he and others took bribes totalling $10m for South Africa to host the tournament and an undisclosed sum for Morocco’s unsuccessful bid to host the 1998 event.
The revelation is contained in a plea bargain published by the US department of justice.
Safa is angered by the reports and believes they tarnish both the reputation of the organisation and some of the country’s most prominent personalities.
The statement read: “We categorically deny that this was a bribe in return for a vote.
“It belittles the hard work done by Madiba [Nelson Mandela], Archbishop Tutu, the South African government and numerous others who sacrificed their time and money and family lives to make our country proud! It tarnishes their images in the most unscrupulous manner.”
Safa sent a letter in 2008 to Fifa secretary general Jerome Valcke saying that $10m should be administered directly by Warner, who is currently on bail in Trinidad pending extradition to the US.
Meanwhile, the head of Fifa’s audit and compliance committee has reportedly claimed Russia and Qatar could lose the right to host the World Cup if evidence emerges of bribery in the bidding processes. Domenico Scala, who is the independent chairman of Fifa’s audit and compliance committee, told a Swiss newspaper if anything untoward was uncovered, there could be the most serious of repercussions.
“Should there be evidence that the awards to Qatar and Russia came only because of bought votes, then the awards could be cancelled,” he is quoted as saying.
In May, seven Fifa officials were arrested in Zurich and charged by US authorities along with two other Fifa officials and five corporate executives over allegations of racketeering, wire fraud and money-laundering.