According to reports in the Daily Mail, the striker has been linked with moves to Russia, as well as Turkey or even join David Beckham and Thierry Henry at America's MLS in June when his contract runs out.
But Terek are the most serious suitors of the star, who has also been linked with their rivals, Anzhi Makhachkala.
Anelka himself is unsure of his own future, having said to his club's official website: "I am linked everywhere but, when you are linked, it doesn't mean you want to leave.
"I like Chelsea and first of all wanted to stay - that's why I am still here.
"I will see what happens in December and, if I am still here, I will see what happens in June.
"I am happy here, I like the club, everyone here, and, after, I will see what happens. It is not only down to me.
"I have been here almost four years now, and I am pleased with the way it has been. It could have been even better but I am still happy", the Frenchman concluded.
However, with Chelsea keen to make space on the wage bill as a result of UEFA's financial fair play regulations that kick in this season, he may find a big money offer from Russia too tempting to resist.