Private Lynch is recovering in hospital in the US
The big four US TV networks are reportedly battling to win the exclusive story of former Iraq prisoner of war Jessica Lynch.
ABC, CBS, NBC and Fox are going to great lengths to get an interview with the 20-year-old US army private, the New York Times said.
The paper said she had been sent gift items and offered TV projects as inducements to tell her story - a suggestion strongly denied by at least one of the media giants.
Private Lynch's rescue from an Iraqi hospital on 1 April turned her into a heroine in the US.
Nine of her comrades were killed when her convoy was ambushed outside Nasiriya. Private Lynch was taken to the local hospital.
Eight days later US special forces stormed the hospital, capturing the events on a night-vision camera.
The rescue was extensively reported around the world.
However, the BBC's Correspondent programme has alleged the US military misrepresented the facts of her rescue.
The programme said the story of her rescue was "one of the most stunning pieces of news management ever conceived" - a charge denied by the Pentagon.
Private Lynch, a supply clerk from Palestine, West Virginia, is recovering from her injuries at a hospital in Washington DC.
She apparently has no recollection of what happened.
The New York Times said that NBC News' high-profile presenter Katie Couric had sent her a bundle of patriotic books - while ABC News rival Diane Sawyer had sent a locket with a photograph of Private Lynch's home.
The paper also said CBS had mentioned a series of possible projects involving other divisions of its corporate parent, Viacom.
It said CBS had offered several MTV specials, a Country Music Television
special, a made-for-TV movie, a possible book deal and a TV interview.
But a CBS spokesman said: "CBS News does not pay for interviews and it maintains a well-established separation from other parts of Viacom."
Jeffrey Schneider, an ABC News vice president, said every news organisation wanted Private Lynch's story.
"It's self evident that we've been in contact with her as has every other news organisation on the planet Earth," he said.