A spokesman for oil and gas sector contractor MODEC told SBS on Monday the boat was spotted off Dampier by workers on a tanker. It had entered the 500-metre exclusion zone around an oil rig, some 140km off the coast.
Premier Colin Barnett said it was always concerning when asylum seeker boats got close to shore, but the matter was under control.
"The West Australian police is looking after that situation until the Commonwealth naval vessel arrives, so the situation is in order," he told reporters.
"This boat, while it's approaching our coast, it's well offshore and it's under surveillance."
It had been reported that the Australian Maritime Safety Authority would fly out to assess the situation, but AMSA declined to comment.
The Department of Immigration and Border Protection referred questions to Immigration Minister Peter Dutton, but his spokeswoman said it was a long-standing policy that the government did not comment on operational matters.

A screenshot from FlightRadar24 taken shortly after 3pm appearing to show a DeHaviland Dash-8 Q300, registration VH-ZZG - operated by Surveillance Australia – off the Western Australian coast. Source: (FlightRadar24)
The reported sighting comes almost two years to the day after another asylum seeker boat sailed close by an oil and gas facility about 200km from Dampier.
Mr Barnett also expressed concern about that incident at the time, saying he understood the boat had been tied up to the floating platform.
But Customs denied this, saying the asylum seekers had only waved at workers on the vessel. They were sent to Christmas Island.
Prime Minister Tony Abbott told Liberal Party members last month that "for almost 12 months there have been no boats whatsoever".
Asylum seeker arrivals since 1992

A boat suspected of carrying asylum-seekers has been spotted off the WA coast. (SBS) Source: SBS
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