The 40-year-old Brazilian 1994 World Cup winner said in Rio de Janeiro that he was considering the Adelaide offer.
"We have had a first telephone conversation with Adelaide United and we will have another next week," he told TV Globo.
"I will see what happens. It is a possibility but there is nothing yet concrete."
Football Federation Australia officials have said they are assessing the paperwork.
Adelaide United coach John Kosmina, who was on the bench when a Romario hat-trick dumped Australia from the 1988 Seoul Olympics, said his club would be honoured to work with Romario if the deal came off.
"For me it would be a privilege to work with him. For the players it would be a privilege, too. Especially Fernando (Adelaide's Brazilian striker)," Kosmina told papers in Australia.
"He's a poacher. I don't expect him to get up and down the park, and he can poach all he wants," the current Australian assistant coach said.
"The fact is, you don't get players of his ilk becoming available very often. He's still playing regularly, he's still got a lot to offer.
Romario's obsession with following countryman Pele as the only player to score more than 1,000 career goals is behind the move.
Off to The City of Churches?
However the task does border on farce when one considers that despite the striker claiming he needs to score 18 more goals to reach the 1,000 mark for his career, official figures on his professional goals put him at the 507 mark.
Many training matches at former Brazilian club Vasco de Gama were apparently scheduled as friendlies to allow the marksman to build on his tally.
It gets more complex when it is factored in that Vasco have bought the rights to his 1,000th goal.
Having rejected Newcastle Jets' approach to register controversial English striker Stan Collymore as a guest player early this week, A-League head of operations Matt Carroll has declined to give Romario a stamp of approval.
"The Romario paperwork has just arrived, so we will give it to our High Performance Unit, and we will also be assessing the commercial part of the arrangements," Carroll told the Sydney Morning Herald.
"But I do note he is still playing regular football, as distinct from the other player (Collymore) and he hasn't got the same track record as the other guy, either."
Should the deal go ahead, it is likely the player will make his Adelaide debut away on November 25, and complete his Australian sojourn when Adelaide play three consecutive home games leading into Christmas.