The billionaire Chelsea owner is yet to have his UK visa renewed after it expired last month, a source close to the oligarch has confirmed to Sky News.
An application for it to be renewed has been lodged but the process is taking longer than usual, the source added.
It comes amid heightened diplomatic tensions between Russia and the UK in the wake of the Salisbury spy poisoning, along with recent British military involvement in Syria.
The British government would not be drawn on the circumstances surrounding Mr Abramovich’s investor visa application, stressing: “We don’t discuss individual cases.”
Downing Street said visa applications from Russia are handled “rigorously and properly”.
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.
A committee of MPs released a hard-hitting report on Monday, accusing Mr Putin and his allies of “hiding and laundering their corrupt assets in London”.
More from World
US and China trade war put ‘on hold’ after progress made in negotiations
The fight to leave the ‘open air prison’ of Gaza
Man shot dead in Dublin by police investigating woman’s disappearance
Jailed British-Iranian Nazanin Zaghari-Ratcliffe told she ‘will be convicted’ on new charges
Arrests after Frenchman ‘lynched’ in front of families in Pau park
NASA’s planet-hunting TESS spacecraft swings by moon, takes picture of 200,000 stars
Responding to the report, Moscow accused Britain of unprecedented “anti-Russian mania”, warning such an attitude could backfire and scare off foreign investors.