The Turkish giants released a statement on their official website, www.fenerbahce.org, in which they said they had informed the stock market about negotiations over Meireles. Fenerbahce would be able to buy the 29-year-old outside the British transfer window because their own country's does not close until midnight on Wednesday.
Chelsea were not immediately available for comment on the claim about Meireles, who only moved to Stamford Bridge from Liverpool for a reported £12million on transfer deadline day last year.
Since then, the Portugal international has struggled to hit top form and has been in and out of the starting line-up.
He has long been linked with a move away and there have been reports in the past week that Fenerbahce were preparing an £8million bid for him.
Letting the all-action Meireles go would be risky strategy by Chelsea, whose midfield was completely overrun by Atletico Madrid in Friday night's UEFA Super Cup debacle.
That evening saw them allow Michael Essien to join Real Madrid on a season-long loan, and with Josh McEachran also out on loan, they are arguably short of cover for John Obi Mikel and Frank Lampard in the anchorman positions.