The Barcelona star suffered the injury in his country's final warm-up match, a 6-0 rout of Poland, on Tuesday, making him a serious doubt for the Group H opener against Switzerland.
"He is coming along well," Spanish Football Federation sources said, following a scan on the injury, while the player himself was optimistic.
"The coach and I have been speaking on a daily basis on how things are going and the level of discomfort and things are getting better and better," said Iniesta. "If I feel good then why not play? I am feeling in good shape."
If Iniesta does not make it from the start then Spain have a ready-made replacement in the shape of Arsenal's Cesc Fabregas.
Iniesta sat things out at training on Saturday while Xabi Alonso, who has a slight leg muscle tear, withdrew some 15 minutes before the end of the session as a precaution and then restricted himself to jogging at the Spanish training camp at the University of Potchefstroom.
On Sunday, he joined training with the rest of the squad but retired half an hour before the end of the session.