The Turkish giants released a statement on their official website 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 about Fenerbahce's announcement over Meireles, who only moved to Stamford Bridge from Liverpool for a reported £12 million 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 £8m bid for him.
Letting the all-action Meireles go would be a risky strategy by Chelsea, whose midfield was completely over-run by Atletico Madrid in Friday night's UEFA Super Cup debacle.
Michael Essien has joined 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.