The former Japanese international midfielder is on a reported AUD$500,000 (USD$528,000) a season deal but wants to activate a clause in his contract to keep him at the Wanderers for a second season, the reports said.
Ono, 33, said he was not motivated to stay in the A-League for financial reasons, but for the standard of football and Sydney lifestyle.
"Yes, I want to (stay) but actually I have just a one-year contract, and we have to speak about next season," Ono told The Sydney Morning Herald.
"I don't care how much the contract (is worth), but if they give me a chance to play I want to do what I can possibly do."
Ono said he had yet to begin talks with the A-League newcomers about extending his stay but hoped that negotiations would start in the coming weeks.
"I don't know (when talks will begin) but I hope soon. I want to stay more," Ono said.
Ono has gradually adjusted to the Australian competition and was man-of-the-match in last Saturday's 2-0 win over cross-city rivals Sydney FC.
"I think my confidence is getting better every day," he said.