The Australian Open moved to Melbourne Park in 1988
Sydney intends to bid for the right to host the Australia Open when Melbourne's contract expires in 2016.
Melbourne hopes to keep an event which is worth about £38m to the economy and has been held in the city since 1972.
But the New South Wales government is considering building a new stadium at Sydney's Glebe Island to capture the first Grand Slam in the calendar.
Tennis Australia's chief executive, Steve Wood: "We completely understand Sydney's interest in our event."
New South Wales chief executive Geoff Parmenter confirmed Sydney's interest.
"The Australian Open is arguably the best annual event in Australia," he told the Sydney Morning Herald.
"I think any events company in the country would be negligent if they didn't have it somewhere on their radar.
"The Glebe Island site is the subject I think of quite a bit of interest because it is pretty much the last clear piece of prime harbour-side real estate left."
No formal bid has been lodged but Parmenter confirmed discussions have taken place.
And Wayne Kayler-Thomson, who heads the Victorian Events Industry Council, urged the Victoria government to fight to keep hold of the event.
"The government must pull out all stops to try and retain this event by improving infrastructure at Melbourne Park," he said.
"It is disappointing that NSW cannot be original and seek their own events instead of trying to cannibalise other Australian cities."
John Brumby, the leader of the ruling party in Victoria insisted: "It's a great stadium, the players love Melbourne.
"We've got the best sports precinct in the world and I don't think we need to take too seriously the threats that are coming from Sydney.
"We're working with (Tennis Australia) to make improvements and we'll be making some announcements about that next year."
With Shanghai, Dubai and Abu Dhabi also reportedly keen to host a Grand Slam event, Wood added: "The bigger and better the Australian Open in Melbourne becomes, the more attractive it becomes to other major cities around the world."
The Australian Open is the first of the four Grand Slam events and is held in the height of the country's summer.
This year's event, which saw Maria Sharapova and Novak Djokovic crowned champions, achieved the highest ever day/night attendance record for any Grand Slam tournament of 62,885.