The pressure is on Prime Minister Scott Morrison to elevate Tasmanian Senator Richard Colbeck to his new Cabinet.
Tasmania is credited with playing a huge part in the Coalition's surprise win after taking the seats of Braddon and Bass from Labor.
A promotion for the North-West based Senator Colbeck would be seen as a fitting tribute to the Liberals' success in returning the Coalition government.
Political analyst Professor Richard Herr said Tasmania should be rewarded with a federal cabinet position.
And the front-runner is North-West based Senator Colbeck.
Professor Herr said Tasmania had played a major part in the surprise election result for the Liberal Party.
"It should be recognised and it would be politic and prudent to have a Tasmanian in cabinet," Professor Herr said.
"It would help to cement the Northern electorates of Braddon and Bass in Liberal hands because we know that they are volatile seats.
"Senator Colbeck is the logical choice."
The last Tasmanian voice in federal cabinet was Liberal Senator Eric Abetz who was Minister for Employment and Leader of Government Business in the Senate.
However, Senator Abetz was dumped by former Prime Minister Malcolm Turnbull in 2015.
Some observers believe that Senator Abetz has proven cabinet ability and should not be ruled out.
However, Senator Abetz was a vocal supporter of former Prime Minister Tony Abbott.
Professor Herr said with Mr Abbott losing his seat, less hard-line views could be more appealing.
He said from a Tasmanian point of view it was important to have a voice in cabinet.
"The cabinet also has a big influence on the COAG decisions and a lot of state issues are subject to the COAG process," Professor Herr said.
Senator Colbeck said he was honoured to lead the Tasmanian team that saw Gavin Pearce, Bridget Archer and an additional Liberal senator in Claire Chandler elected.
"This election victory has also been a remarkable endorsement of the leadership of our Prime Minister and, if offered, I would humbly accept any opportunity to continue to serve as a member of the ministry in the re-elected Morrison Government," he said.
"The people of Braddon and Bass have endorsed our Government's plan and we will deliver for them."
Senator Colbeck was appointed Assistant Minister for Agriculture and Water Resources by Mr Morrison last year.
Senator Abetz and colleague Senator Jonathon Duniam declined to comment on speculation about who Mr Morrison would appoint to cabinet and the ministry.
Re-elected Labor member for Lyons Brian Mitchell said Tasmania should be represented in cabinet.
"Absolutely, because Tasmania has been forgotten for the past six years, and we need a voice to talk about jobs, cost of living and health," Mr Mitchell said.