Barnett had earlier fought the charges, but after a failed bid to have the counts dismissed, she is expected to enter a guilty plea during a court appearance in Charlestown, South Carolina, next Tuesday local time (Wednesday NZT), The Post and Courier reported.
She would then be sentenced by US District Judge Richard Gergel, according to court records seen by the newspaper.
She faces up to 30 years in prison.
Barnett's lawyer Russell W Mace III said she was "hoping for a positive resolution to the case", The Post and Courier said.
"My client is looking forward to completing this part of the criminal process."
It's understood Barnett indicated during a proceeding on Tuesday that she planned to change her plea.
Barnett has been behind bars since her arrest more than 14 months ago, and her supporters say her health has deteriorated during that time. She was denied bail late last year, but still holds out hope of being reunited with her daughter.
"She's looking forward to seeing her daughter, whether it's in the courtroom or once she's eventually released from jail," Mr Mace said.
Her daughter and friends in Australia have publicly supported her, saying she was trying to protect Savanna when she fled the US.
Barnett accused her former husband Benjamin Harris Todd III of abuse during their divorce proceedings, but a judge ruled there was no evidence of her claims and granted him full custody of the child.
Barnett left her home with Savanna during a court-supervised visit in April 1994 and never returned.
The former flight attendant was reported to have fled the US with the help of Faye Yager, founder of shadowy organisation Children of the Underground, which helped women escape allegedly abusive relationships.
Denying bail last year, US Magistrate Judge Bristow Marchant said in court documents she "willfully and through a course of careful planning abducted a minor child from the lawful custody of her father, left the United States, and for the last 20 years has engaged in extensive travel to various countries through the use of multiple false identification documents in order to avoid detection".
