The US wants to try Mr Warner, 72, a Trinidadian national, on corruption charges. He is accused of accepting millions of dollars in bribes.
He and 13 other current or former Fifa officials were indicted in May.
He denies the charges and is currently fighting the extradition attempt.
Last week, Switzerland approved the extradition of ex-Fifa Vice-President Eugenio Figueredo to the US.
Mr Figueredo, from Uruguay, was arrested in May while in Switzerland for a Fifa congress.
So far, only one arrested official – former Fifa Vice-President Jeffrey Webb, from the Cayman Islands – has agreed to be extradited.
After being extradited from Switzerland to the US, Mr Webb pleaded not guilty to accepting bribes worth millions of dollars in connection with the sale of marketing rights.
He was placed under house arrest on $10m (£6.4m) bail by a New York judge.
The king of Caribbean football
As the head of Caribbean and North and Central American football (Concacaf), Mr Warner was one the most powerful men in world football.
His support was seen as essential for any World Cup host bid. However, he has been dogged by allegations of corruption.
The US alleges that Mr Warner has been involved in corrupt practices for more than two decades.
Mr Warner’s case has been adjourned until Friday due to a legal dispute over a technicality.
In June 2015, a BBC investigation found evidence of bribes paid to Mr Warner.