"Representatives of the oligarch have travelled to Saudi Arabia and Dubai to elicit interest in the club," The Sunday Times said, referring to Gulf sources.
According to the paper, at least one of the meetings was held with members of the Saudi royal family but there has been no evidence so far of a potential buyer.
However, a Chelsea spokesman said that it was "total nonsense" that the Russian billionaire was willing to sell the club, the paper reported.
Abramovich's wealth has fallen sharply amid the ongoing global financial crisis. Philip Beresford, who compiles The Sunday Times Rich List, conservatively estimates that Abramovich has lost 3 billion British pounds ($4.4 billion) from his fortune of 11.7 billion pounds ($17 billion), the paper said.
"City experts question whether he may have a short-term problem with liquidity and needs cash," the paper said.
