The 41-year-old actor was giving information at the phone hacking trial at the Old Bailey, when he was asked by former NOTW editor Andy Coulson’s lawyer Timothy Langdale if he was aware that a member of his "immediate family" had talked to the newspaper.
Jude Law arriving at the Old Bailey to give evidence in the phone hacking trial
The question was asked in relation to a story written in 2005 about Jude's then-girlfriend Sienna Miller having an affair with Daniel Craig.
"I was aware later around 2011, maybe later than that, at the time I was approached about the case that the NOTW had been in contact with people in my family, trying to find things out, asking quotes," he said.
Asked if he knew the family member was getting paid, he replied, "I have never been aware of that, getting paid for it."
The actor pictured with Sienna Miller in May 2010
Timothy Langdale then told the court he did not intend to publicly identify the family member, and wrote the person's name on a piece of paper, which was then handed to Jude in the witness box.
The actor didn't react as he read the name. He was then asked again if he was aware this specific person was selling stories.
"I was made aware very recently there had been some kind of communication with this person and several others in and around the time, this period. I was never aware any money changed hands," he said.
Later, when was asked by prosecutor Andrew Edis QC when did he first find out money had allegedly changed hands, he replied: "Today."
Jude and his ex-wife Sadie Frost
Jude told the court that the media had "an unhealthy amount of information" about his life, and said that photographers would turn up at places where he had secretly arranged to take his children.
Press attention began to intensify when he was nominated for an Oscar in 2001 for The Talented Mr Ripley, he told the jury. It grew throughout his divorce from Sadie Frost and then during his relationship with Alfie co-star Sienna.
"The daily appearance of packs of photographers either on the street or in cars became a very regular occurrence," he revealed.
Jude also said that when police showed him notes that private investigator Glenn Mulcaire had on him, he was "shocked" by the amount of information accumulated.
Former News of the World editors Rebekah Brooks and Andy Coulson are on trial accused of conspiring to hack mobile phones, charges they deny.
There are seven defendants in total, with some of them facing allegations of illegal payments to public officials and, separately, allegations of attempts to hide potential evidence. All seven deny the charges.