"Within a week after Labor Day there will be a hearing... so in early September," Meghan Bartley, legislative aide of the state's committee on election law, told AFP.
"They have to figure out if they will change the current law. Every member of the (Massachusetts) House and Senate will attend the hearing."
Before his death Tuesday, Kennedy had urged his home state to change the law to allow someone to take his place temporarily in the US Senate ahead of a special election for his seat, not now due before January.
Governor Deval Patrick, who has supported the proposal, was due to hold a press conference Monday at 3:00 pm (1900 GMT).
Kennedy's death after a 15-month battle with brain cancer robs the Democratic Party of its crucial 60-seat majority in the Senate, just as lawmakers are set to return next week to debate bills on health care reform and climate change.
President Barack Obama has pushed lawmakers to draft legislation radically overhauling the US health system, which currently leaves some 47 million people uninsured.
But the proposals have triggered a storm of grassroots protest, leaving their passage in the US Congress uncertain.
Kennedy, who had thrown his support behind Obama, made health care reform one of his lifelong causes, and mourners at his funeral on Saturday, including one of his grandsons, urged that the campaign go on.
Some observers have called for Kennedy's senate seat to be temporarily filled by his widow, Vicki, until new elections can be organized. But she is said not to be interested.
The Boston Globe reported Monday that Joseph Kennedy, a former congressman and son of Robert Kennedy who was assassinated in 1968, could now run to replace his uncle.
"Joe Kennedy, as emotionally drained as he must be, cannot help but be moved by the outpouring of affection and respect that has come from people all over the country in the last several days," Dan Payne, a longtime Democratic media consultant, told the daily.
"I'm not saying he is going to run, but he wouldn't be human and he wouldn't be a Kennedy if he didn't give serious thought to running for the so-called Kennedy seat."
Other names being mentioned are veteran Democratic politicians Edward Markey, Michael Capuano and Stephen Lynch.
Current Massachusetts law, enacted in 2004, mandates a special election 145-160 days after a vacancy occurs, which means the primaries would be held in December with an election in January.
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