The mother of the unborn baby has been identified as model Samantha Burke, who has listed her due date on an online gift registry as 6 October (09) - the same day his eldest child, with actress Sadie Frost, turns 13.
Reports suggest the British actor and Burke had a fling at the beginning of 2009 when Law was shooting Sherlock Holmes in New York.
The pretty brunette is said to be seven months pregnant.
An online baby gift registry, obtained by TMZ.com, also suggests Burke is expecting a baby girl she plans to name Sophia.
Law's publicist has already denied online reports the sister of Law's Sherlock Holmes co-star Rachel McAdams is the mother of the actor's unborn child.
A statement from Burke's attorney reads, "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.".