The Russian has been barred from entering the UK after failing to obtain a visa.
Abramovich threw his Chelsea future in doubt after ripping up his plans for his £1bn Stamford Bridge revamp.
It's understood he is not willing to commit a huge investment into the capital city of a nation where the government does not want to give him a visa.
But if he's thinking of selling the club, he'll bank a wedge.
He has already pumped in over £1bn since buying the London team for £140million in June 2003.
And he will want to recoup the money he has put into Chelsea when he eventually cashes in.
According to Forbes, Chelsea is the seventh most valuable club in the world worth £1.44bn.
The Times report that the oligarch would want to see the £1.17bn he's put into the club repaid by any potential new owner.
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Abramovich gained Israeli citizenship earlier this week, meaning he no longer needs a visa to enter the UK — although he can only do so as a visitor and not in a working capacity.
He oversaw the plans to knock down the Bridge and replace it with a 60,000-capacity stadium on the site of the club’s home since it was founded in 1905.
A terse statement issued without warning said: “Chelsea Football Club announces today that it has put its new stadium project on hold.
“No further pre-construction design and planning work will occur. The club does not have a time frame set for reconsideration of its decision.
“The decision was made due to the current unfavourable investment climate.”
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