"I would be indebted to you for life," she said. "I would write you a cheque for the entire portion (of a condominium) I own in Australia."
In the taped conversations, Monica Lewinsky also says she was told to deny an affair with the president.
In the transcripts, Ms Lewinsky says someone told her: "It doesn't matter what anybody says, you just deny it."
However, she does not say who the advice came from.
She says she feared for her life if she did not sign an affadavit denying having an affair with the president.
Fears as story broke
The transcripts also reveal how Ms Lewinsky became anxious as her affair with Bill Clinton became public.
At one stage, Ms Lewinsky says: "It's just too - it's too much for one person."
Mrs Tripp, her colleague at the Pentagon who secretly taped the conversations, agrees. "Oh, it's too much for one person," she says.
Both Ms Lewinsky and Mrs Tripp were subpoenaed by Mrs Jones' lawyers.
Ms Lewinsky submitted an affidavit denying a sexual relationship with Mr Clinton.
Mrs Tripp filed an affidavit saying that Ms Lewinksy had confided to her that she did have an affair with Mr Clinton.
Independent Counsel Kenneth Starr used the tape to win permission to expand his investigation to include the Lewinsky matter, an investigation that has now led to impeachment proceedings.
Ms Lewinsky received immunity from prosecution by Mr Starr in exchange for her testimony before a Grand Jury in August.
Lewinsky testimony - video extracts
Monica Lewinsky's evidence
Impeachment debate: Key quotes
The Monica tapes: Confiding in a friend
Highlights: More evidence
Lewinsky urged Tripp to lie
President's secretary was reluctant witness
Highlights: The video
The infamous dress
Secret meetings with Clinton
Touching moments