Citing unnamed US and Pakistani officials, the newspaper said US officials were eyeing areas surrounding the Pakistani city of Quetta, where the Taliban leadership is believed to be hiding.
But the request also seeks to expand the boundaries for drone strikes in the tribal areas, the report said.
On Friday a US drone attack destroyed a vehicle in Pakistan's tribal district of North Waziristan, killing at least three suspected militants, Pakistani security officials said.
The United States considers Pakistan's tribal belt an al Qaeda headquarters and the most dangerous place on Earth, and has reportedly criticised Pakistan's failure so far to launch a major ground offensive in North Waziristan.
Friday's drone strike comes three days after a similar attack killed at least 15 militants and destroyed a training centre north of Miranshah.
More than 220 people have been killed in Pakistan in over 40 strikes since September 3.
But The Post said Pakistan has rejected the request. Instead, the country has agreed to more modest measures, including an expanded CIA presence in Quetta.
"You expect us to open the skies for anything that you can fly," the paper quotes a high-ranking Pakistani intelligence official as saying. "In which country can you do that?"
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