The Rabbitohs - across seven games at Olympic Park and 13 at AAMI Park - have never beaten the Storm in Melbourne.
But Craig Bellamy's side are nearing uncharted territory as they prepare to host Souths on Friday, having lost five-straight games for the first time since 2012.
The Bunnies' formline (4-2) has been up and down, but after Latrell Mitchell led a massacre of St George Illawarra last week there's a golden opportunity for Wayne Bennett's men to break their Victorian drought.
"I honestly try not to think too much about records or any hoodoos or anything like that," Rabbitohs captain Murray said.
"It's always a big challenge going down to Melbourne - they've been the top team, the pinnacle of this competition, for a long time.
"Playing them in their backyard has proven to be a little bit extra hard coming up against a team like that.
"They're always strong, Melbourne. We always have to be on our A-game and we have to be ready to work hard for a win."
Melbourne five-eighth Cameron Munster conceded this week that he was in an unprecedented form slump.
But Murray expects the Storm, who have suffered successive losses to Brisbane, North Queensland, Penrith, the Warriors and Canberra to right the ship eventually.
"Melbourne have got the talent and the skill across the park to be dangerous regardless of how they've started the season," Murray said.
"They've got some world-class players in that team, so we certainly won't be taking them lightly and we'll certainly be preparing for a good Melbourne team."
Papua New Guinea international Alex Johnston will play his 250th game and is hoping to continue his strong tryscoring form - the winger has crossed 17 tries in 15 games - against the Storm.
"We can't have one week on, one week off sort of thing," Johnston said.
"We really need to knuckle down and play our best footy this week.
"We definitely need to go down there and get our first win in, I don't know how long it was, 20 games or something."
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