The moderate Cronulla MP has his party's support to become opposition leader, however speculation also surrounds the fate of Mr Morrison's federal southern Sydney electorate of Cook.
Mr Speakman is yet to confirm whether he will actually run to replace former premier Dominic Perrottet, with Alister Henskens and conservative Anthony Roberts the other names put forward.
The three are considered the party's most experienced MPs following the coalition's March 25 election loss but so far only Mr Roberts has confirmed he will contest the leadership.
Labor's new Environment and Energy Minister Penny Sharpe on Monday accused the Liberals of leaving their portfolios in chaos in the wake of the defeat.
"As we're getting our feet under the desk, it is very clear that there are a lot of problems in a lot of areas that we are inheriting," she told reporters.
"No wonder the opposition can't find themselves a leader.
"They have left a mess for all of the incoming ministers and they probably don't want to stand up and actually face the music about what they've left behind."
It comes as rumours swirl that Mr Morrison will announce his retirement.
Six Liberals said the former prime minister planned to quit politics after the federal budget in May and confirmed the decision to people in his electorate, according to the Sydney Morning Herald.
In NSW, a party room meeting to decide a new leader is still likely more than 10 days off, as counting continues in the state's upper house.
Mr Perrottet and his inclusive style was well-liked among colleagues and its understood the party sees who it next chooses as leader as critical to its future.
The major coalition partner secured its 36th seat on Saturday, with Jordan Lane winning Ryde by a margin of just 50 votes from Labor's Lyndal Howison. She is considering requesting a recount and will make a decision on Wednesday.
Outgoing Liberal Minister Victor Dominello previously held Ryde by almost nine per cent.
AAP has contacted Mr Speakman's office for comment.
