Fame Daddy says that 40 famous faces, including a rock star, a "genius", a Formula 1 racing driver and a former footballer, have signed up to offer their sperm.
Fees for the "premium insemination service" start at £15,000, The Sun reports.
The website explains that prospective parents can give their child "a head start in life" by using sperm from "a proven winner".
Fame Daddy chief executive Dan Richards said: "What we are selling is the sperm of people who are successful, who have risen to the top of their field.
"Our aim is to provide excellent levels of medical care in a supportive and nurturing environment. We will offer a range of top quality celebrity surrogate fathers whose contributions are exclusively available at our fertility clinic.
"Whether it is talent on the stage or pitch, having a world-beating voice, or just being very beautiful, Fame Daddy will have the perfect celebrity surrogate daddy."
A member of the House of Lords, an Oscar-winning actor, an Olympic gold medallist and a successful entrepreneur have also allegedly signed up Fame Daddy, although it's unknown if the site is a spoof.