The 33-year-old, who has a special lifetime contract at Barca, is expected to leave Camp Nou at the end of the season and had been strongly linked with a move to China.
Iniesta's signature would be a significant coup for the little-known Chinese side and the latest in an influx of top-tier foreigners following big-money signings in recent years.
"I am positive on introducing Iniesta," Gong Daxing, chairman of the club's title sponsor SWM, told the Xinhua news agency.
"Iniesta's arrival would be beneficial for Chongqing and a great bonus for our brand."
The Spain legend intends to reveal the decision over his future by the end of the month.