Ms Berejiklian will remain premier until the Liberal Party elects a replacement.
Planning minister and Pittwater member Rob Stokes - who has been described as a key ally of Ms Berejiklian - wants that to be him.
Speaking to reporters outside his home on Saturday, the 46-year-old said he'd been talking to his colleagues about his leadership ambitions and was encouraged by the level of support so far.
Mr Stokes - who was elected in 2007 and has also served as minister for environment and transport - is expected to go up against frontrunner, Treasurer Dominic Perrottet.
"I think Dom has strong claims to the job and he's putting them out there ... but I believe I have the qualities necessary to provide strong government into the future," Mr Stokes told the ABC.
"I think I owe it to my community and our to the people in NSW to at least
provide them that choice," he told 7News.
Mr Perrottet said on Friday he would speak with his family and colleagues over the coming days on "how I can best serve the people of NSW", praising Ms Berejiklian as one of NSW's finest ever premiers.
Mr Stokes also commended Ms Berejiklian on Saturday, expressing sadness over the end to her career and promising to abide by the roadmap out of lockdown that she unveiled only weeks ago.
"Gladys Berejiklian has provided an extraordinary example of leadership and of stability and it would be my intention to continue (the plan) as laid out, particularly in relation to the opening up," he told the ABC.
Other potential contenders include Environment Minister Matt Kean and Tourism Minister Stuart Ayres.
Either would be the first Liberal leader from an area outside of Sydney's north or east in almost two decades, if elected.
Transport Minister Andrew Constance and Attorney-General Mark Speakman have also been spoken of as possible candidates.
Whoever succeeds Ms Berejiklian has a tough act to follow.
Prime Minister Scott Morrison led the tributes on Friday, lauding her "heroic" qualities and saying she was a "dear friend" and trusted by the community.
Meanwhile supportive constituents have gathered outside her home with flowers and balloons in her initials while others stood outside her office with handmade signs reading "We love Gladys" and "Long live Gladys".
Ms Berejiklian's leadership endured bushfires, drought and storms and she navigated COVID-19 but after four-and-a-half years in the top job, she couldn't beat ICAC.
The anti-corruption watchdog says it is investigating whether she "exercised public functions" in a position of conflict given her secret five-year relationship with ex-MP Daryl Maguire, revealed at its hearings in late 2020.
Mr Maguire is accused of abusing his public office between 2012 and 2018.
A wearied Ms Berejiklian said on Friday she had "no option" other than to resign, as she could not temporarily step aside and resume her role after the investigation.
Her resignation "could not happen at a worse time," she said, as the state prepared to leave months of COVID-enforced lockdowns in less than two weeks.
She continues to deny any wrongdoing.
"History will demonstrate that I have always executed my duties with the highest degree of integrity for the benefit of the people of NSW, who I have had the privilege to serve," she said.