Outgoing Tasmanian Premier Will Hodgman hasn't formally endorsed a successor but has given glowing praise to his long-term deputy in a probable sign of his preference.
The state is expected to find out next week who will become the Apple Isle's 46th premier after Mr Hodgman's sudden resignation on Tuesday.
The logical frontrunners for the role are Deputy Premier Jeremy Rockliff and fellow senior minister and Treasurer Peter Gutwein.
Mr Hodgman will himself vote on the next leader before he officially steps down.
He was coy when asked if Mr Rockliff had his endorsement.
"I'm not presuming to endorse anyone," Mr Hodgman told ABC Radio on Wednesday.
"I'll allow my colleagues to determine individually what their intentions are.
"Jeremy Rockliff, as I've said, is not only a wonderful deputy for those 14 years that he's sat alongside me in parliament ... but he's a mate. I've known him for many years."
The state Labor opposition labelled the delay in appointing a new premier as a sign of internal division.
"The Liberal Party is clearly dysfunctional and there is a lot of tension. We need this to be resolved quickly," Labor leader Rebecca White said.
Like Mr Hodgman, Mr Rockliff was first elected to parliament in 2002.
The next state election is due to be held in 2022, with Mr Hodgman saying a mid-term exit was the right time for fresh leadership.
He has signalled a desire to spend more time with wife Nicki and their three children having spent 18 years in politics.
Mr Hodgman has hailed the state's economic turnaround under his leadership but those successes have been offset by a shortage of affordable housing, lengthy hospital waiting lists and questions about how the island best manages a tourism boom.
"Whoever (is next) has got a big job ahead of them," Ms White said.
"This government has let a lot people down. If you look at our health and housing system.
"There's a real challenge ahead to ensure some of the economic indicators are transitioned across to improving social indicators, so that all people are able to benefit."
Mr Hodgman comes from a line of Liberal politicians with his father and grandfather also serving in state parliament.
Greens leader Cassy O'Conner has backed Mr Rockliff, who she described as kind and having a big heart.
Australian Associated Press