Now it has emerged Florida-based aspiring model and actress Samantha Burke is the mother-to-be.
In a statement released to US celebrity website TMZ.com her lawyers said: "Ms Burke can confirm that she did in fact have a relationship with Mr Law and that she has informed Mr Law that she is expecting his child later this fall".
"Since informing Mr Law of the pregnancy, he has been nothing but responsive and supportive of Ms Burke and the pregnancy."
There has been no comment from Jude, who is currently single, on these revelations.
Twenty-four-year-old brunette Samantha is reportedly due to give birth to the actor's daughter on October 6 and plans to call the baby Sophia. Once the baby is born, Jude apparently wants to make monthly trips to Pensacola, in Florida, where she lives.
She is believed to have had a short romance last Christmas with Jude while he was working in New York on Guy Ritchie's Sherlock Holmes film.
Jude already has three children – Rafferty, 12, Iris, eight, and son Rudy, six – from his seven-year marriage to Sadie Frost. They divorced in 2003.
He announced news of the pregnancy on Wednesday, saying he would play a "fully supportive" role in the child's life, despite no longer being involved with the mother-to-be.