The allegations were first made public last month, but several Israeli news sources said the country's Civil Service Commission has begun looking into the claims.
"The commission is investigating whether Packer's gift amounted to receipt of an illegal benefit or favor," Haaretz newspaper reported.
The article, which cited a story by Israel's Channel 10, said Mossad chief Yossi Cohen received seven concert tickets "worth thousands of shekels", and had been given free use of Mr Packer's Tel Aviv apartment.
The article also said Mr Cohen had been interviewed by the agency, which will release a report on the matter.
SBS had contacted a spokesperson from Mr Packer's gaming empire Crown Resorts for comment.
Last month, Israeli media also reported that Mr Packer gave members of Prime Minister Benjamin Netanyahu's family lavish gifts, along with benefits like use of his private jet.
The Times reports that Mr Packer is believed to be seeking permanent residency in Israel. The Times article speculates that this could be to take advantage of a 2008 law exempting new immigrants from paying tax on their foreign assets for ten years.
Israel's interior minister Aryeh Deri said the billionaire had made a preliminary application to the Israeli tax agency.
It's been a tough year for Mr Packer, who recently ended his relationship with fiancee Mariah Carey.
In October, more than a dozen employees who were marketing Mr Packer's foreign casinos were detained in China, where gambling is illegal.
