"We're looking at something happening in the next 30 days," newspaper Jamaica Gleaner quoted Paulwell as saying. The minister has just returned from Brazil.
Of Jamaica's 20 offshore and four onshore blocks - each 2,500 sq km - eight offshore blocks are under license. Australian company Finder Exploration holds five blocks and Canada's Rainville Energy three.
The minister said Petrobras was examining the remaining blocks.
Petrobras would be able to explore for five years under state energy company PCJ's standard agreement offered to exploration firms. Should it strike oil, the Brazilian company would be allowed 20 years of extraction rights under a profit sharing agreement that could see PCJ retain 12.5%, the report added.
During his visit to Brazil, Paulwell also renewed a memorandum of understanding that calls for Petrobras to provide technical assistance on ethanol and biodiesel.
"I think we should be seeing some experimental crops this time next year and once that is successful, then we could see the start of processing," he said.
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