According to Adelaide's The Advertiser, the City Council this week settled on a formal position and will send a letter to the State Government asking them to look into a return.
Adelaide was Australia's first Formula 1 host, the Grand Prix running on the city's streets from 1985 to 1995, before it moved to Melbourne for the 1996 event and beyond.
Adelaide now hosts V8 Supercars on a shortened circuit.
"We'd just like to see the State Government take the steps to see if it is viable and whether a pitch could be made," Councilor Alex Antic was quoted by The Advertiser.
Tourism Minister Leon Bignell, however, has already slammed the idea, describing the make-up of Adelaide City Council as "the most infuriating people in South Australia".
"How about they put in some money so we can get the grandstands up a bit quicker, which will make their ratepayers happy?" he was quoted by the publication last week.
"Look at Bathurst; their council put in $6 million. These clowns put in $50,000 and charge us $100,000. They are big on complaining but not putting their hands in their pockets.
"We're not interested in it [hosting the Grand Prix again]."
Melbourne has a deal to host the Australian GP until 2023.