The director of Chinatown and The Pianist hopes that testimony by a prosecutor will back his claim that he reached a plea deal in the case that would keep him out of prison, his attorney Harland Braun told the AFP news agency.
But his French lawyer Hervé Temime said he would not attend the unsealing of a transcript next week for fear of being arrested.
Polanski was accused of drugging 13-year-old Samantha Gailey - now Geimer - before raping her at film star Jack Nicholson's house in Los Angeles in 1977.
Polanski admitted having unlawful sex with her and went to jail but broke bail conditions to flee the country after his release because he believed that Judge Laurence Rittenband wanted to go back on the agreement and make him spend up to 50 years in prison.
He wants "acknowledgement that he has already executed his sentence" in the United States, in order to "freely travel and have his arrest warrant lifted", Temime said.
Polanski was arrested in Switzerland in 2009 on a US extradition request and spent 10 months under house arrest before Bern rejected the US order.
Poland's Supreme Court turned down another extradition request in December, ruling that he had served his time under the plea deal.
Braun believes the secret testimony of prosecutor Roger Gunson collected in 2010 in the US supports Polanski's claim that he had an agreement to serve just 48 days and that, taken with the Polish decision, it should convince the US authorities Polanski has served his time.
"After we confirm the contents, we will urge the court to recognise the Polish decision resulting from a litigation initiated by the [district attorney] and in which the DA participated," Braun told AFP.
"If the court accepts the principle of comity, Roman can come to Los Angeles and to court without fear of custody."
He wishes to visit the grave of his ex-wife, Sharon Tate, who was murdered while pregnant by the Charles Manson sect in 1969, according to his lawyers.
Polanski became a French citizen in 1976 and lives in France with his current wife, Emanuelle Seigner.
In January he withdrew from presiding at France's version of the Oscars, the Césars, after feminists threatened to picket the ceremony over the rape case.