Mr Speakman has the party's support the become state opposition leader as rumours surround the former prime minister's plans for his southern Sydney seat of Cook.
The Cronulla MP and moderate is yet to confirm if he will run to replace former premier Dominic Perrottet as Liberal leader, with the party also putting forward Alister Henskens, and conservative Anthony Roberts.
The three MPs are considered the party's most experienced MPs returning to parliament after the coalition lost the March 25 state election, and were put forward by the party as potential successors. So far, only Mr Roberts has confirmed he will contest the leadership.
It comes as rumours swirl that Mr Morrison is considering announcing his retirement.
Six Liberals said the former prime minister had decided he would resign from politics after the federal budget in May and confirmed the decision to people in his electorate, according to the Sydney Morning Herald.
Mr Perrottet and his inclusive leadership style was well-liked among his colleagues, and its understood the party sees their choice of leader as critical to their future direction.
The party room meeting is still likely more than 10 days away, as counting continues in the state's upper house.
It comes after the party secured its 36th seat, with Liberal candidate winning the electorate of Ryde with a margin of just 50 votes over Labor's Lyndal Howison.
NSW Labor is considering requesting a recount in Ryde, and will make a decision on Wednesday.
Outgoing Liberal Minister Victor Dominello previously held Ryde with a margin of close to nine per cent.
AAP has contacted Mr Speakman's office for comment.
