Samantha Burke is eight months pregnant with baby Sophia after dating the British star while he was shooting new movie Sherlock Holmes in New York earlier this year (09).
According to the New York Post, Burke is in talks with an American weekly magazine and a U.K. newspaper for exclusive photos of the newborn and an interview with the 24 year old about the pair's brief relationship.
The story is reportedly set to coincide with Law's run as Hamlet on Broadway. He will make his debut in the play on 6 October (09) - the same day Burke is due to give birth.
A source tells the New York Post, "Samantha is getting offers ranging up to $200,000 (£133,333). The irony of the timing for the interview is not lost on her. She will talk openly about her relationship with Jude."
A spokesperson for Burke has declined to comment on the reports.
Law - who already has three kids from his former marriage to actress Sadie Frost - has vowed to stand by the baby.
Burke's spokesperson confirmed in August (09): "Samantha, her mum and her family can confirm Jude has been responsive and supportive through the relationship and pregnancy and know that he will remain so as a father once baby Sophia is born."