The 48-year-old, his nation's all-time leading goalscorer before Lionel Messi overtook him last year, is wanted as a replacement for departing Spaniard Guillermo Amor.
Adelaide chief executive Grant Mayer said capturing Batistuta was a priority given former Barcelona star Amor had decided to leave.
"We're chasing a suitable replacement after Guillermo Amor has all the respect and goes out on his own terms," Mayer told the Adelaide Advertiser newspaper.
"With Batistuta an offer has been made, but there is also a Plan A, B and C."
Batistuta, regarded as one of the best strikers of his generation, scored 56 goals in 78 games for Argentina, and netted more than 200 for Fiorentina in Italy's Serie A.
The flamboyant Argentine, who lived in Australia from 2007-11, has no top-level coaching experience.
Disclaimer: No Business Standard Journalist was involved in creation of this content