Eremenko quit the Rugby Park club after a season-long campaign in 2010/11 to return to Rubin Kazan. The 30-year-old was sent off twice during a controversial stay at Kilmarnock while Mixu Paatelainen was in charge.
"I have had offers from clubs in Scotland, China and Japan," said Eremenko. "I could easily play for any of the clubs in Scotland, except, perhaps, Celtic.
"I still have three or four years left as a player, so my next move is very important."