The club's official website announced that legal proceedings had begun in the High Court. Chelsea FC are also a claimant in the legal case.
A statement on the Chelsea website said that Abramovich had no intention of selling the club.
"Mr Abramovich has already made quite clear, through the directors of Chelsea, that he has no intention of doing so and that neither he nor anyone upon his behalf has been pursuing any such course of action," read the statement.
Quoting "Gulf sources," the Times article in question said that "representatives of the oligarch have travelled to Saudi Arabia and Dubai to elicit interest in the club."
Abramovich's wealth has fallen sharply amid the ongoing global financial crisis. The Bloomberg news agency estimated in October that the oligarch had "lost $20 billion, based on assets excluding property and cash."
The former governor of the Chukotka Autonomous Area in Russia's Far East bought Chelsea in 2003. The side has won the English Premier League twice since then.