His UK investor visa reportedly expired some weeks ago but the British government has refused to comment on his individual case.
An official at Nativ, a department of Prime Minister Benjamin Netanyahu's office dealing with Jewish communities in the ex-Soviet Union, said Abramovich had applied for an immigration visa at Israel's embassy in Moscow, the station said earlier on its website.
The British governemnt has declined to comment.
'In total, Abramovich spent about three hours in Israel, ' stated the report.
The country's interior ministry has confirmed Mr Abramovich has gained citizenship there, The Times of Israel reports.
Israeli media reports say he has been given an identity card in Israel under the Law of Return, which allows Jews to become citizens of Israel.
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Abramovich returned to Russian Federation when his UK visa expired, meaning he could not be present to see Chelsea lift the FA Cup for the eighth time in the club's history with a 1-0 victory against Manchester United at Wembley last weekend.
The delay in issuing him a new one comes amid increased diplomatic tensions between London and Moscow after the poisoning of former Russian spy Sergei Skripal in southern England. Unlike the Russians, the Israelis do get a visa-free stay in the United Kingdom for up to six months straight, but it's not clear if the decision on the Tier 1 investor visa that he needs is actually affected by the citizenship of the applicant.
Abramovich has been a regular visitor to Israel and Ynet said he had bought a property that was formerly a hotel, in an old Tel Aviv neighbourhood close to the Mediterranean shore.
The story was headlined: 'Roman Abramovich has become a new immigrant to Israel'.
He has own Chelsea football club since 2003.