Mr Kennedy was a longtime champion of healthcare reform
Massachusetts lawmakers are to consider a rule change allowing the state governor to pick an interim successor to the late Senator Edward Kennedy.
Under current law, the seat will remain vacant until a special election, which will not be held for several months.
Senate Democrats are worried that a lengthy vacancy could make passing a healthcare reform bill more difficult.
Before his death last week Senator Kennedy, a Democrat, made it clear that he supported a change in the rules.
Massachusetts Governor Deval Patrick, also a Democrat, has indicated that he supports the proposal.
The Massachusetts legislature will hold a public hearing on the issue on 9 September, after which a bill could be rushed through to implement the change.
Following Edward Kennedy's death, the Democrats have 59 votes in the US Senate.
Sixty votes are needed for the party to ensure that the minority Republicans cannot use procedural delaying tactics to block legislation.
Mr Kennedy's nephew, Joseph, is a possible candidate for the post
Mr Kennedy was a long-time champion of universal healthcare and his supporters are determined to make sure that his death will not jeopardise the passage of President Barack Obama's healthcare reform bill.
Governor Patrick has announced that the special election to select a replacement for Mr Kennedy will be held on 19 January.
Among those named as possible contenders for the vacant seat is Mr Kennedy's nephew, Joseph Kennedy II, a former congressman.
Analysts say if he does run, it could put off other candidates, unwilling to run against a Kennedy so soon after the senator's death.
Family sources have said Mr Kennedy's widow, Victoria Reggie Kennedy - who had been thought a potential candidate - is not interested in running, the Associated Press reports.