Structural separation would force Telstra to split into two distinct companies, with separate boards and executives - one operating as a network wholesaler and the other as a retailer.
Their hopes were buoyed by such statements in the Government's regulatory reform paper as: "Maintaining the current separation arrangements will not deal with the issues concerning Telstra's use of its vertical integration. In light of this, there are a number of options the Government is considering."
But neither the Communications Minister, Stephen Conroy or Shadow Communications Minister Nick Minchin will openly advocate a Telstra split.
Conroy refused to advocate the structural separation of Telstra during a dogged late night grilling by Minchin at a Senate Estimates Hearing late last week.
At around 10pm on May 26, Minchin repeatedly asked Conroy and Patricia Scott, secretary of the Department of Broadband, Communications and the Digital Economy, for their position on the matter.
Both Scott and Conroy replied that structural separation was never explicitly mentioned in the regulatory reform discussion paper.
"I do not believe I have ever advocated it," Conroy said. "Telstra may volunteer it. Who knows? There is a new regime in town.
"I am not advocating it," he later said. "I have never advocated it."
Instead, Conroy said the Government "does not have a predetermined view" on the matter will "have an open mind about the reforms that should be pursued."
For his part, Shadow Minister Senator Minchin said the Opposition is definitively opposed to the structural separation of Telstra.
"Any decisions regarding structural separation should be left to the Telstra board and its 1.6 million shareholders," Senator Minchin said.
A spokesperson for Senator Minchin elaborated further today.
"The Minister [Conroy] likes to give the impression structural separation of Telstra is on the table - creating the perception that he is wielding a big stick," he told iTnews. But away from the public glare, late at night in Senate Estimates, he says it's not even on the table."