A report in Wednesday's Daily Mail suggests that the deal for the event is being facilitated by former Renault team principal Flavio Briatore.
The race would take place around the streets of Azerbaijan's capital, Baku.
"We're going to Azerbaijan," Ecclestone said.
"The people out there [in Azerbaijan] are talking about holding a race in 2015."
"That may be a bit soon — unless it's at the end of the season, that's a possibility. But 2016 is more likely."
Azerbaijan is one of a number of countries targeting hosting a Formula 1 race within the next few years.
The twice postponed American Grand Prix around the streets of New Jersey remains in contention for 2015, while Mexico and India are both planning a return to the calendar.