But a lawyer for the social media influencers has accused UK authorities of failing to provide the documentation required in support of the applications for them to be removed.
The requests were lodged with the US State Department last week.
It is reviewing the extradition applications to ensure they are compliant with the existing treaty between London and Washington.
Once this process has been completed, the applications will be sent to the US Justice Department which will in turn forward it to the court, where the final decision on their extradition will be made.
An official letter from the State Department details that Andrew Tate, 39, is "wanted to stand trial in the United Kingdom" on a series of charges, including 10 counts of rape, three counts of arranging or facilitating trafficking for sexual exploitation and three counts of assault occasioning actual bodily harm.
He is also accused of making and distributing indecent images of a child and possessing extreme pornography.
Charges levelled against Tristan Tate, 38, include five counts of rape, six counts of assault occasioning actual bodily harm, three counts of sex trafficking and a sexual assault.
Both men deny any wrongdoing.
The brothers' lawyer, Joe McBride, said he would be challenging the requests, arguing they were not backed up by the information needed under the provisions of the extradition agreement between the UK and the US.
Speaking to the Press Association on Wednesday: "They haven't told us anything we didn't already know. There's no supporting facts.
"The truth is we are unsurprised.
"This is the level of arrogance you get from governments with unchecked power."
The Tates learned last week that they must stay in jail as they fight their extradition to the UK.
Judge Lauren Louis said they had "failed to meet their burden to demonstrate that they do not present a risk of flight or danger to the community, or that special circumstances warrant their release".
It means the controversial pair will remain behind bars in Miami during what could be a lengthy legal process aimed at securing their removal to Britain.
The former professional kickboxers, who hold dual US and British citizenship, have been held in custody since their arrest in July.
They were detained after more charges were brought against them by UK prosecutors.
The Tates are deeply divisive figures, who have built a massive online following – mainly among young men and boys – to which they have been accused of promoting misogyny and toxic masculinity.
During a court hearing in August, the Tates maintained their innocence and argued their brash online personas were characters and not their true personalities.
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