Despite tabling a bid, Nice president Jean-Pierre Rivere has admitted he aims to keep hold of the 27-year-old.
"West Ham approached us with an offer which was of no interest. Eric Mouloungui is an important player and we want to keep him," BBC Sport quotes Rivere as saying.
However, the Frenchman admitted they would be open to selling the player if the right bid came in.
"Obviously if it's an acceptable offer on different levels we're not stupid, we'd study it, but it's not the case," he added.
The frontman, who has entered the final year of his contract, has admitted that he would consider making the move to Upton Park.
"I'm a Nice player and I'm happy to continue here but anything is possible between now and the close of the transfer window," he said.
Mouloungui scored eight goals last season, making him Nice’s top scorer.