The troubled Malaysia state-investment fund 1MDB was back under the microscope Thursday with claims that the stepson of the prime minster had used cash from the fund to buy a London property, according to the Wall Street Journal who cited people familiar with the situation.

The report states that PM Najib Razak's stepson Riza Aziz - a film producer and founder of Red Granite Pictures - purchased a house in central London in 2012 with money originating from the 1Malaysia Development Bhd (1MDB) fund. It adds that the redbrick four-story property is worth £23.25 million ($33.6 million) and is located in London's exclusive Belgravia neighborhood. The Journal said that Aziz had denied any wrongdoing, as had Najib. Both did not immediately respond when contacted by CNBC for comment.

The report adds to a long-running saga surrounding the state investment fund, which is currently being investigated by local and international officials for alleged corruption and money-laundering. 1MDB teetered on the verge of default in 2015 after racking up 42 billion ringgit ($11 billion) in debt in just five years.

1MDB's outlook took a twist in July last year, after the WSJ reported that $700 million had been transferred from the fund to the prime minister's personal bank accounts back in 2013. Najib has repeatedly denied any wrong-doing. In January, he was cleared by the Malaysian Attorney General after a probe found that the money came from the Saudi royal family.

Read the full WSJ article here.

—CNBC's Pauline Chiou and Nyshka Chandran contributed to this article.