In a week in which Wayne Bennett's side lost star centre Latrell Mitchell for the next month with a fresh calf injury, veteran five-eighth Walker shone brightly in front of 14,365 at CommBank Stadium on Thursday.
The 36-year-old, who outpointed NSW State of Origin five-eighth Mitchell Moses, scored a brace and set up Euan Aitken, but remains without a deal for next year.
"I think he'd like to play on if he could, we'd like him to play on if he can and right now it's looking good for him," Bennett said.
Walker was the man to put the game to bed in the 62nd minute, going over for his second try at a time his side were looking vulnerable.
Winger Ed Kosi had limped off with a thigh injury midway through, while fullback Jye Gray was sent for a head injury assessment after a head clash with Eels centre Sean Russell.
Despite passing his test late in the game, Gray wasn't needed as Walker sliced through the Eels' line and Souths (8-6) chalked up a valuable win ahead of a meeting with Penrith next Friday.
"I enjoy coaching him, he's a bit slow learning what a six to go is and being onside but we'll win that battle," Bennett said.
"He's got God-given things that you can't coach and he's a great competitor."
While the Rabbitohs were disciplined and workmanlike, the Eels were anything but.
Parramatta looked to have made solid progress in recent weeks but Thursday's showing felt like a step backwards in captain Mitchell Moses' 250th NRL game.
Coach Jason Ryles was visibly frustrated as his side (5-10) made 17 errors, missed 36 tackles and had a 60 per cent completion rate.
Asked why his side had regressed so dramatically from a win over Canberra a fortnight ago, Ryles said: "If I had some answers for you I'd give them to you.
"Our good's good, and our bad is just nowhere near good enough."
Walker scorched through for the opening try in the fifth minute, the playmaker then setting up Aitken for his next magic trick to give the Bunnies a 12-0 lead with a quarter of an hour gone.
Moses set up Brian Kelly to make it 12-6 at the break before Parramatta squared the game after halftime through Tallyn Da Silva.
Kosi crossed on the right to re-establish a buffer in Souths' favour before Russell was placed on report for kicking Tallis Duncan as he crashed in on the same edge.
Walker burst through for his second with less than 20 minutes to go with Duncan collecting a brace in the dying stages to wrap up victory.
7°C