The 65-year-old Swede was expected to take over from Al Nasr coach Walter Zenga after the former Italy goalkeeper's contract was terminated on Saturday.
However, Eriksson said he was leaving too, with local media linking him to Chinese Super League Club Guangzhou R&F.
"I'm leaving Al Nasr, and Dubai," Eriksson was quoted as saying by The National newspaper.
"I have done what I set out to do: I looked at football schools, academies and the first team, and I've given my advice on everything, such as how to get the best out of the academy and other details.
"So that part of the job is done. Now it's up to the club to do it or not. But from my side it's done," said the Swede who joined the club in January on an 18-month contract.
On his future, Eriksson said: "I might also have a possibility to go back into coaching somewhere. You will know that in a couple of days."
Asked if it would take him to China, Eriksson replied: "Maybe, but there are other solutions."
As well as England, Eriksson had spells with Mexico and Ivory Coast at international level, and Benfica, Roma, Sampdoria, Lazio and Manchester City at club level.
- Sports & Recreation
- Walter Zenga