To fill the vacancy left by Senator Inouye's passing Democratic party officials have begun discussing who they will pick for three possible appointees.
Governor Abercrombie says they have 21 days to do so. Then he will make the final selection.
In his final letter to Governor Neil Abercrombie, Senator Inouye said he would like to see Congresswoman Colleen Hanabusa succeed him.
Hanabusa said today: "I am honored Senator Inouye has mentioned my name... but I also want to respect the process set forth in Hawaii law. Right now, I believe our focus should be on honoring Senator Inouye and his tremendous contributions to Hawaii and America."
To fill a vacancy, a U.S. Senator is appointed, as are State Senators and Representatives. But if there's a Congressional vacancy, that would trigger a special election.
The last statewide special election was in May 2010 to fill Gov. Abercrombie's Congressional seat.
Councilman Charles Djou held the seat for six months until Hanabusa won a full term that November. It cost the state $625,000
Chief Elections Officer Scott Nago says a special election next year would cost the state a lot more.
"You need to remember that was in an election year, so there were some costs that was born on by the regular election," Nago said. "For example, there was staff that we didn't need to bring on because we already had staff for the regular election this year."
Nago says if a special election is held once the office secured the staff, equipment, and money, he would issue a proclamation.
The election would then be conducted within 60 days.
He says the special election would likely be all mail-in voting, and the winner would hold that seat until the next election in 2014.
According to the Associated Press, Hawaii Democratic Party Chairman Dante Carpenter says the party hopes to have a new senator in Washington for the first day of the new congressional session on Jan. 3, 2013
Carpenter met with Gov. Neil Abercrombie Monday to discuss a successor to Sen. Daniel Inouye. Carpenter said he discussed the mechanics of the process with Abercrombie.
The party's state central committee, which has about 80 members, will likely meet by conference call to select the three candidates. But Carpenter said the party isn't looking to do that this week, as it wants to respect Inouye's family and the contributions Inouye made.