The DR Congo international still has two years left on the four-year contract he signed after joining from Toulouse in 2009.
Ilunga is now being linked with a move out of Upton Park following relegation with a number of Ligue 1 clubs also interested.
Newly-promoted QPR and Norwich are reportedly keen on the 29-year-old, but the Toffees, Wolves, Rennes and former club Toulouse are also believed to be ready to join the hunt.
Ilunga is aware of the speculation and while he has no problems with West Ham, he would like to continue playing top-flight football
"I'm aware of the speculation," he told skysports.com. "Nothing's done at the moment. I want to play in the top division.
"West Ham's a friendly club and I'm very happy to play for them, but you never know in football."