A report by the BBC said that Piddle Valley, Lytchett Matravers and Corfe Castle are among nine sites suggested by energy companies.
The Oil and Gas Authority announced last week 27 locations in England where licences to frack for shale oil and gas would be offered.
A further 132 blocks nationally have been subjected to further detailed environmental assessment under EU law, including the sites in Dorset.
The findings of this assessment are now out for public consultation, and more offers for licences will be made later in the year.
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Drilling For Oil in Lytchett Matravers