The Russian billionaire did not attend Saturday’s FA Cup final, in which Chelsea beat Manchester United.
A source close to the oligarch confirmed to Sky News that Mr Abramovich’s visa expired at the end of April.
An application for it to be renewed is in process but taking longer than usual, they added.
Mr Abramovich’s spokesman, John Mann, refused to comment.
The oligarch owns property in London but has now returned to Russia, explaining his absence from Saturday’s football showpiece, according to website The Bell.
Flight records show the businessman’s personal Boeing 767 airplane was last in London on 1 April, the publication added.
The Home Office would not comment on Mr Abramovich’s visa status.
Security Minister Ben Wallace said: “We do not routinely comment on individual cases.”
Mr Abramovich is worth an estimated £9.3bn, according to the Sunday Times Rich List, and has overseen an era of lavish spending at Chelsea since taking charge of the London club in 2003.
He has links to Vladimir Putin’s government in Moscow and, earlier this year, was included for the first time on a US list of Russian officials and oligarchs close to the Kremlin that could serve as a basis for future sanctions.
The UK government has toughened its rhetoric against the Kremlin since the nerve agent attack on Sergei and Yulia Skripal in Salisbury in March.
At the time, Russian opposition leader Alexei Navalny claimed sanctions against Mr Abramovich would be “very effective and supported by public opinion within Russia”, as part of a UK response to the Skripals’ poisoning.
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He also named Arsenal part-owner Alisher Usmanov and former deputy prime minister Igor Shuvalov as other possible targets for sanctions.
The Russian government is currently planning new laws that would make the promotion of Western sanctions by Russian citizens a criminal offence.