The 33-year-old Irish actor's girlfriend Alicja Bachleda-Curus was reported to have given birth to a baby boy.
The 26-year old Polish actress went into labour a week ago in Los Angeles, the reports said.
In an interview with the Polish tabloid 'Super Express', her brother Tadeusz said: "I am delighted my little sister has given birth. I hope that before the end of the year, I can fly out to see my new nephew."
The Hollywood couple were said to have kept the birth secret for almost a week and have refused to reveal the name of their newborn son.
However, there was no confirmation from Farrell's agent last night.
Two years ago, Farrell opened his heart and revealed that his five-year-old son James is a special-needs child.
The actor described how the condition has affected his speech and mobility.
James, who is from Farrell's previous relationship with Kim Bordebave, has a rare form of cerebral palsy called Angelman Syndrome.