Russian state news agency TASS and other media picked up a report on The Bell website, which said an acquaintance of Abramovich and two in his inner circle had told it the billionaire's British visa ran out three weeks ago and he is waiting for a new one.
Amid a spiralling diplomatic crisis between Britain and Russia over the poisoning of a former Russian double agent, there have been calls in Britain for sanctions that would hurt super-rich Russians who have homes in London.
Abramovich formally has residency in Jersey in the Channel Islands, a tax haven, but has never taken it up. The Sunday Times put his wealth at 9.3 billion pounds ($12.5 billion) on its Rich List this year. He has owned Chelsea since 2003.
Abramovich's spokesman John Mann told AFP he could not comment because "it's a personal issue." Mann gave the same response to TASS.
The Bell published the Russian-language report on Sunday. It said it had received "no comment" responses from Abramovich's spokesman and the Home Office.
AFP also requested a comment on the issue from the Home Office in London, but none was immediately forthcoming.
The report quoted a source in Abramovich's entourage as saying that Britain had not refused to issue a new visa to Abramovich but was considering his application.
Russia's Sport-Express website cited sources in Abramovich's entourage as saying that it had taken a long time for his application to be processed but he was due to get a new British visa shortly.
The Bell was started by the former editor-in-chief of the RBC media group, Elizaveta Osetinskaya. Under her leadership, RBC was known for high-profile investigations.
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