The spot became available on Saturday when upper house MP Peter Poulos was dumped after it was revealed he had shared explicit pictures of rival during a preselection battle.
Mr Elliott, who is from the party's centre-right faction, announced his retirement last year after failing to secure sufficient support to keep his seat after a redistribution.
However, less than five weeks until voters go to the polls Mr Elliott says the unexpected vacancy in the upper house could be a pathway to revive his political career.
"I told the premier I would like to be considered," he told Sydney radio 2GB on Monday.
"But the Liberal Party being what it is we have to go through processes, that's appropriate, that's proper," he said.
Premier Dominic Perrottet is under pressure to get more Liberal women into parliament and could intervene to ensure that happens.
The vacancy could also resurrect the career of Holsworthy MP Melanie Gibbons, who lost preselection in her seat.
Treasurer and moderate faction powerbroker Matt Kean was quick to signal he was "doing everything I can to ensure that a woman fills that casual vacancy".
On Friday, the government was caught up in a second scandal when Damien Tudehope resigned as finance minister after declaring he owned shares in toll road owner Transurban, the company that operates most of Sydney's toll roads.
Meanwhile, the government announced on Monday it would offer incentives of up to $4000 to public school teachers, in a bid to encourage more to gain national Highly Accomplished and Lead Teacher accreditation.
Education Minister Sarah Mitchell said the accreditation would recognise highly effective, innovative and exemplary teaching and enabled teachers to achieve salaries of up to $120,000.
"We want to make it as easy as possible for our best teachers to be recognised and remunerated for their impact," Ms Mitchell said.
"There are already 310 (of the accredited teachers) in NSW, but we have an ambitious goal to increase the number to at least 2,500 by 2025."
However, Labor says the government's latest election-eve cash splash would not solve the classroom crisis that was driven by chronic teacher shortages and crippling administration tasks.
Labor's education spokeswoman Prue Car says it's "too little too late from a tired, 12-year-old government that is out of ideas and throwing money out the door five minutes before an election".
"Election-eve cash splashes won't solve the classroom crisis that is driven by chronic teacher shortages and the unsustainable admin burden that has built up on our teachers."
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