According to The Times, representatives of the oligarch have travelled to Saudi Arabia and Dubai to elicit interest in the club.
At least one of the meetings was with members of the Saudi royal family. There has been no evidence so far of a potential buyer.
The Middle East has become the cash cow for British football teams.
One source said: Abramovich’s team have been out in the Middle East sounding out what interest there is in buying the club.
Chelsea, however, insisted last night that Abramovich was still fully committed to the club on which he has lavished hundreds of millions of pounds.
A Chelsea spokesman said it was total nonsense that the Russian was willing to sell the club that he had bought for about 60 million pounds in 2003.
Sources say that if Abramovich can recoup his money, he might now be ready to sell after five years in which he turned Chelsea into a Champions League side that has twice won the English Premier League.
Part of the reason for considering such a proposal is the fact that Abramovich’s wealth has fallen sharply in the global downturn.
Philip Beresford, who compiles The Sunday Times Rich List, conservatively estimates that Abramovich has lost three billion pounds of his 11.7 billion pound fortune.