Manager Andy King has lost Brian Howard, Grant Smith and Matt Heywood, but Igoe does not want to follow them out of the exit door.
He said: "I wasn't happy with Swindon's original offer, and it's not a case of being greedy.
"Other clubs have shown an interest but I want to stay at Swindon and if they budge just a little I'll sign and stay I'll sign without a doubt.".