Murray trained with a no-contact bib on at Souths practice on Wednesday, just two weeks after he underwent surgery on his shoulder.
He faces a fitness test later this week before a decision on whether he plays against Wests Tigers on Saturday night, just 24 hours before Brad Fittler names his NSW team for the Origin series opener on June 8.
NSW and South Sydney teammate Damien Cook insisted a healthy Murray would be able to handle Origin even if he didn't play against the Tigers.
"I just hope that with Cam the type of person is ... he's 100 per cent right to go and not pushing anything (for Saturday)," Cook said.
"Freddy (Fittler) would know that Cam is going to do the job in Origin.
"He's very professional about everything he does. He's only been off for a couple of weeks. and been training hard anyway.
"I don't think that (an extra game) is something that Cam needs with the type of player he is and the type of person he is."
Murray would shape as a massive inclusion for both the out-of-sorts Rabbitohs and injury-plagued Blues if passed fit.
NSW must already replace two centres, with Tom Trbojevic and Latrell Mitchell injured, while prop Daniel Saifiti, second-rower Tariq Sims and utility Jack Wighton are no certainties to be picked.
Centre remains the point of most conjecture, with Stephen Crichton and Kotoni Staggs the favourites to debut.
Fittler's close ally Phil Gould on Wednesday called for Matt Burton to be picked, reasoning the Canterbury half was Dally M Centre of the Year alongside NSW's core at Penrith in 2021.
Cook also argued for Souths teammate Campbell Graham, after he was part of Blues camps last year.
"He (Graham) is our best player this year by far," Cook said.
"You talk about Origin and coming off your line for most of the game ... Campbell Graham is someone I look to as my go-to man to get us out of trouble.
"He's one of the best defensive centres in the game at the moment too."
Second-rower Keaon Koloamatangi shapes as Souths' other NSW hope, depending on the make up of the Blues bench after spending time in camp last year.
"It gave me a lot of confidence and you can probably see it with my football last year and this year too," Koloamatangi said.
"I'm now trying to be a leader for the team.
"While I was in the camp I learned to be more professional, and not being a kid anymore."
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