The Chelsea football club owner has been waiting several weeks for his United Kingdom investor visa to be renewed.
The official was not authorized to talk to the media and spoke on condition of anonymity.
"Roman Abramovich arrived at the Israeli embassy in Moscow like any other person", an Israeli government spokesperson told Channel 10 "He filed a request to receive an immigration permit, his documents were checked according to the law of return, and he was indeed found eligible".
Worth an estimated £9.3 billion, according to the Sunday Times, Abramovich would become the richest person in Israel and would be exempt from the country's taxes on income earned overseas for 10 years, as well as not being required to declare the source of that income.
Spokesmen for Netanyahu's office contacted by AFP did not confirm or deny the report.
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"He landed today in his private aircraft at (Tel Aviv's) Ben Gurion airport and was presented with an Israeli identity card", the commercially-owned station said on its evening newscast.
Abramovich owns the Varsano boutique hotel in Tel Aviv's Neve Tzedek neighborhood, which he bought for NIS 100 million in 2015 and is converting into his Israeli home.
One of the world's richest men - his visa is taking "longer than usual" to get renewed.
Israeli passport holders can enter Britain without a visa for short stays, although they require visas to work there.