A journalist in American Samoa says the United States government wants the territory to be more independent.
The US Congress may get to vote on a bill which would give the Fono the authority to override the governor's veto.
Since it would require changing the territory's constitution, there would also need to be a public vote.
A Radio New Zealand International correspondent, Fili Sagapolutele, says the public may be leery about such a change, but the US could welcome it.
"It's something that the US Department of Interior has raised over the years, that they'd like to see the territories be able to maintain a lot of control within their borders. I'm sure they're going to be able to approve whatever comes out of American Samoa if the voters approve it."
Fili Sagapolutele says voters may not want to give new powers to the unelected Senate.