So far only 31% of the votes have been counted in a two-question, non-binding referendum.
And the man elected to be the new governor of the island, Alejandro Garcia Padilla, has campaigned in favour of maintaining the status quo.
It is the fourth time in 45 years that Puerto Rico has voted on its national status.
The island is currently a US territory, with US currency and passports.
It has ceded control of its foreign and defence policies to Washington, but governs itself and does not return senators to the US Congress. Puerto Rico is represented in Washington by a non-voting delegate.
On Tuesday voters were asked two questions in a referendum. The first was whether they wanted to change Puerto Rico's relationship with the US. Of the votes counted, 53% were in favour of change.
The second question asked whether islanders wanted to become a US state, gain independence or have a "sovereign free association" that would grant Puerto Rico more autonomy.
Those in favour of becoming the 51st US state hold a clear lead in that ballot, with more than 60% of the vote