The Wall Street Journal has reported the first few subs could be built in the United States.
It said the White House was in talks to expedite the delivery of the vessels to the mid-2030s in a bid to counter China's growing military might.
Peter Malinauskas on Monday said he had spoken to federal Defence Minister Richard Marles, who reaffirmed that an Adelaide build was still on the cards despite concerns any delays could open up a military capability gap.
"It is my firm view ... that anything the government does to address that can't be at the expense of building nuclear submarines in Adelaide as soon as possible," the SA Labor premier told ABC Radio.
Mr Malinauskas acknowledged any SA-built subs would not be ready until close to 2040 but said it was vital to build local sovereign capability.
"We can't always rely on the fact that, in the distant future if there were to be a conflict, we'll simply be able to rely upon overseas partners to acquire that capability," he said.
The premier stopped short of saying whether he expected each of the eight promised submarines to be built locally.
An interim report on Australia's military capabilities and a timeline for nuclear submarines are expected to be provided to Mr Marles in November.
The final recommendations are expected to be handed down in March next year.
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