The Australian outfit are hopeful the experienced attacker is willing to follow in the footsteps of Alessandro Del Piero by moving 'Down Under'
The 37-year-old World Cup winner has a contract with the Giallorossi until June 2016 and a transfer seems unlikely due to the forward's popularity at the Stadio Olimpico.
Nevertheless, Fong is hopeful that Totti is willing to follow in the footsteps of former Italy team-mate Alessandro Del Piero and leave Serie A for the Australian top flight.
"It would be great for Brisbane Roar if we could sign a great champion like Totti," Fong told Corriere dello Sport.
"He is an incredible player and everybody knows him. Del Piero has become an icon at Sydney and Francesco could achieve the same at us. He is already a legend and he will be received like a king in Australia.
"The A-League is on the rise ever since the arrival of Del Piero.
"I know that Totti means to Roma, but you never know what will happen in football."
Brisbane Roar finished fifth in the A-League last term and currently sit atop of the table.