The new contract for the 21-year-old will not end speculation linking Elia with Schalke, Ajax and PSV Eindhoven among others.
"I intend to finish the season with FC Twente, but in the summer I would like to make the step to an even better team," Elia told local newspaper TC Tubantia.
"Why would I sign a new contract when I might be going soon? The contract offer that FC Twente made me, spoke a lot of respect and appreciation."
Elia's agent, Klaus Vink, has confirmed there is an agreement with FC Twente "but we haven't signed anything yet".
Vink added: "I hope that will take place in the coming week, we would like to have it all in black and white.
"The intention is certainly that Eljero stays with Twente this season. Or there would have to be a club willing to pay a gigantic transfer fee for him.
"But that sum must be really high."
Both the player and the club have denied there is a transfer fee clause in the new contract but FC Twente chairman Joop Munsterman admitted: "It's an intelligent contract that gives both parties guarantees, without having a limited transfer fee."