Under the nation's Law of Return, Jews living overseas have eligibility to gain Israeli citizenship.
Immigration enforcement officers police the rules and could act if Mr Abramovich was known to be working at Stamford Bridge or engaging in activity to run Chelsea while in the UK.
Spokesmen for Netanyahu's office contacted by AFP did not confirm or deny the report.
Abramovich flew into Israel early yesterday in his private jet, and received an Israeli identity card under the Law of Return, which allows Jewish people to become citizens of Israel.
The move could pay off financially as new Israeli citizens are exempt from paying tax on foreign income for 10 years. "Israelis are required to obtain a visa if they want to live, work or study in the United Kingdom".
However, Abramovich's representative said that his strong identification as a Jew and his warm feelings towards Israel motivated him to make aliyah.
His UK investor visa reportedly expired some weeks ago but the British government has refused to comment on his individual case.
The Chelsea FC owner "can come as a visitor for six months but will need a visa to live, work or study in the United Kingdom", the spokesperson added. Mr. Abramovich also invests in Israeli startups through London-based investment firm Millhouse LLC, whose portfolio includes Spot.IM, quick-charging battery startup StoreDot Ltd., Video monetization company Anyclip Ltd., venture capital firm iAngels Crowd Ltd., children's mobile entertainment startup Kidoz Ltd. and Israeli-linked rideshare firm Via. The Jewish tycoon will live in Tel Aviv's chic Neve Tzedek neighborhood.