Asotasi ruptured his pectoral muscle back in April against Canterbury and was expected to miss the rest of the season.
However the 30-year-old is back running without pain and will be eased back into contact work over the coming weeks.
The former New Zealand international has his eyes set on returning in a month.
Even if he fails to be back by round 22, he definitely looks certain to be back on the field well before finals time.
The Rabbitohs are also expecting injured duo Matt King and Eddy Pettybourne to return in two weeks' time.
Centre King has been battling hernia problems, while back-rower Pettybourne has been mending a torn calf.
For a second straight season, injuries have ensured South Sydney have had to manage with a largely make-shift forward pack.
Sam Burgess has been in and out of the side all year, and with Asotasi and Pettybourne sidelined, several players have had to play out of position.
Back-rowers Jason Clark, Dave Tyrrell and Ben Lowe have filled in at prop, while hooker Nathan Peats and backline utility Chris McQueen have been packing down in the second row.
Clark, who at 183cm and 101kg is usually outsized in the front row, says he's happy to do whatever job is required.
"For me it doesn't matter where I play I'd be happy to play anywhere," he said.
"Whether it's front row getting bashed I'll take it on the chin and I take it on as a role.
"Same with the other boys, Nathan Peats obviously plays above his weight.
"We don't have a lot of big blokes but I think we play above our weight.
"A lot of people think it's hard for us but we just worry about playing football and our bigger names will run off the back of that and do what they do."
The Rabbitohs have fallen just short of the finals in previous seasons, but currently in sixth place, they're well-positioned for a finals assault.
Clark said it comes down to mentality.
"Rather than thinking we could be there we need to think we should be there," he said.