A Hanabusa aide confirmed she would submit an application to the state Democratic Party, which will select a slate of three potential candidates to succeed Inouye, who died Monday, Roll Call reported.
Gov. Neil Abercrombie, a Democrat, would likely pick Hanabusa if she is among the three, as expected, the Washington publication said. Inouye sent a message to Abercrombie not long before his death saying he preferred her to succeed him.
Inouye's body will lie in state in the U.S. Capitol Rotunda Thursday, the senator's office said. His funeral will be Friday at the National Cathedral, the Honolulu Star-Advertiser reported Tuesday.
Inouye's body will lie in state at the state Capitol in Honolulu Saturday, the Star-Advertiser said.
A final memorial service is scheduled Sunday in Hawaii at the National Memorial Cemetery of the Pacific at Punchbowl, an extinct volcanic crater.
The Senate Appropriations Committee chairman, third in line for the presidency as Senate president pro tempore, had been hospitalized with respiratory problems since Dec. 6.
The U.S. Senate observed a moment of silence for Inouye at the start of Tuesday's session.
Inouye's desk was draped in black cloth and had a vase of white roses on it, a tradition when a Senate member dies.
Senate Majority Leader Harry Reid of Nevada said a lei being sent from Hawaii will replace the roses.