The 28-year-old has been put up for sale at Stamford Bridge but saw a proposed switch to the City Ground fail at the 11th hour on Thursday after Chelsea were said to have not filed the necessary paperwork in time.
Newly-promoted Forest had an agreement in place to pay Batshuayi's wages for the last year of his Blues contract, taking him on a free transfer in the process.
Turkish giants Fenerbahce are now exploiting the situation to try to strike a deal for the Belgian international, who is keen to play regular football ahead of the World Cup in Qatar later this year.
While the transfer window is now closed in England, the market in Turkey remains open until September 8.
Chelsea boss Thomas Tuchel has not even afforded Batshuayi a place on the bench in any of his first five matchday squads this season and sees him as a dispensable member of the squad.
However, the player has been training with the first team at Cobham to keep up his fitness ahead of any potential move.