Ms Maxwell is accused of helping the convicted sex offender Jeffrey Epstein groom young girls, which she denies. She is due to stand trial in July.
In a court filing, her lawyers said she had no desire to leave the US.
She would be willing to renounce her foreign citizenship "to eliminate any opportunity for her to seek refuge in those countries", the filing added.
Her lawyers also proposed that her and her husband's assets be placed in a monitored account, to prevent her being able to use the money to leave the country.
Ms Maxwell has been in jail in Brooklyn, New York, since she was arrested last July at her secluded mansion in the state of New Hampshire.
This is her third application for bail, after two previous attempts were unsuccessful.
In her last bid for bail in December, her lawyers proposed that she be allowed to return home with armed guards to prevent her from escaping.
Prosecutors then said there was a risk that, if bailed, Ms Maxwell could use her wealth to flee to France or the UK where she is a citizen and suggested she might try to avoid extradition.
Ms Maxwell, the daughter of media mogul Robert Maxwell, was in a relationship with financier Jeffrey Epstein in the 1990s. She allegedly introduced Epstein to wealthy and powerful figures including Bill Clinton and the Duke of York, Prince Andrew of the British Royal Family.
Epstein took his own life in prison in August 2019 as he awaited trial on sex trafficking charges, more than a decade after he was convicted for soliciting prostitution from a minor.
Four of the charges against Ms Maxwell relate to the years between 1994 and 1997, when prosecutors say she helped Epstein groom girls as young as 14. The other two charges are allegations of perjury in 2016.
She faces up to 35 years in prison if convicted in her trial in July.
Stop chasing the money and start chasing the passion.