The doctor, who acted as Jackson's dermatologist before the singer passed away last month, is allegedly after guardianship of Prince Michael, 12, and 11-year-old Paris Michael Katherine.
A source told the Sunday Mirror: "Arnie is planning to fight for custody of Prince Michael and Paris. He says he can prove he is their father with Debbie [Rowe] (Jackson's ex-wife)."
The insider went on to reveal that the 'Thriller' star wanted Klein to father his children because of his high level of intelligence. "When Arnie was at college, he would get top marks without having to study - he had a photographic memory and instant recall.
"He becomes more than just a patient's dermatologist - he takes over their health care."
The source continued: "Arnie has told his close friends he is Prince Michael and Paris's father for years, while never giving a straight answer in public. He says he was paid nothing for the sperm but was paid for keeping the information confidential.
"The kids have grown up with 'Uncle Arnie' visiting the house and spending holidays with them."
Jackson's mother Katherine, who it has been suggested has a bitter relationship with the doctor, is currently applying to the court for permanent custody of the children, as well as 7-year-old Prince Michael II (also known as Blanket).
Klein has previously denied donating sperm to the late King Of Pop.