The 76-year-old director was arrested in Zurich last month after travelling to Switzerland to collect an award at the city's film festival, and he has since then been held in custody.
The Swiss justice ministry is reported to have said that if the extradition request was approved that Polanski might appeal against it, although a previous appeal for release on bail has been denied.
Polanski, who is a citizen of France and Poland, originally faced charges for six offences, but following a plea bargain that was struck he pleaded guilty to unlawful sex with the teenage girl.
