New Wallabies coach Eddie Jones proved he meant business late last month by signing Sydney Roosters centre Suaalii to a three-year deal worth an estimated $1.6 million a year from 2025.
Suaalii's new deal has only intensified speculation as to which NRL player could be next to take the leap and Jones has repeatedly identified Murray, a former captain of Newington College's First XV, as high on his wishlist.
Murray is contracted with the Rabbitohs until 2025 but has previously said he would be open to switching back to rugby.
Suaalii's deal is more lucrative than any in the NRL to date but no amount of money in the world will entice Murray into leaving Souths while unfinished business remains.
"Money's never been a massive motivator for me," Murray said.
"My answer to that question (about switching codes) has always been the same and it's been that I wouldn't say no.
"But if I go, and that's a big if, it'll be much later on in my career.
"The motivator for me is what I've always envisioned myself doing in my career and I've ticked a lot of boxes off so far.
"All I've wanted to do was play for Souths and be successful here at the club and strive to win a premiership.
"I'm really hungry to do something like that and I think we've got a great opportunity."
The first step on the road to premiership glory will be ironing out the creases from last week's 18-10 loss to Melbourne.
The Rabbitohs were sluggish in defence and could not break the Storm down in attack, despite repeated chances inside the red zone.
At a loss to explain their lack of intensity post-match, Murray insisted on Tuesday the Rabbitohs now knew where they had gone wrong.
"We're dipping in our toes a little bit in the first 10 or 15 minutes and not starting with the intensity and frontloading with the intensity that we need," he said.
"There are a lot of simple errors for us.
"And I guess just general effort area stuff like kick pressure, kick chase and stuff like that.
"It's all simple fixes and much easier said than done. But like I said, we're pretty optimistic."
The Rabbitohs lose Alex Johnston for the clash with Canterbury on Friday after the veteran winger was concussed against Melbourne.
Headlining the replacement options is Taane Milne, who hasn't played since hitting Penrith's Spencer Leniu high in the 2022 preliminary final and earning a six-match suspension.
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