According to Fox Sports, APIA's strong links to Roma's club academy in Australia could prove pivotal to snaring the 41-year-old for the September 26 clash.
Roma great Giuseppe Giannini is set to be in Sydney for the match, and ensuing academy sessions, and the National Premier League NSW finalists are hopeful that he can convince the recently retired Totti to play.
The news comes just days after fellow FFA Cup quarter-finalist, Avondale were reportedly in talks to sign fellow Italian Andrea Pirlo for a similarly one-off appearance.
However, APIA - who stunned Melbourne Victory in the FFA Cup round of 16 last month - are said to be aware that securing Totti is far from a fait accompli.
Totti amassed 786 appearances for Roma during a 24-year career before confirming his retirement and being appointed to the club board at the end of the 2016-17 season.