Quoting "a US intelligence source", the Sunday Express said bin Ladin and "up to 50 fanatical henchmen" were inside an area 16km wide and deep "north of the town of Khanozai and the city of Quetta".
"He is boxed in," the unidentified source was quoted by the tabloid as saying, adding US special forces were "absolutely confident" he could not escape.
According to the source, bin Ladin moved into the area, "in the desolate Toba Kakar mountains", about one month ago from another area 240km to the south, the Sunday Express said.
In Washington, a Defence Department spokesman declined to comment on the report.
Taliban leader Mullah Muhammad Umar is believed to be with bin Ladin, according to the report.
The area is under surveillance from a geostationary spy satellite while US and British special forces await orders to move in, the newspaper said.
On Thursday, General Richard Meyers, chairman of the US joint chiefs of staff, said US forces were engaged in "intense" efforts to capture bin Ladin, but held back from saying where he might be hiding.
TheTaliban leader is believed to
be hiding along with bin Ladin
"There are areas where we think it is most likely he is, and they remain the same," said Meyers, who was speaking to reporters in Washington.
"They haven't changed in months," said Myers.
Asked whether al-Qaida leader was believed to be in Pakistan, the general replied: "Don't know that. We think in that border region somewhere. We don't know where it is precisely."
The Sunday Express said it was also told in London by "a senior Republican close to the White House and the Pentagon" this past week that bin Ladin had been located.
"They have found bin Ladin," the source - described as an "intimate" of the family of US President George Bush - was quoted as saying.
"They now know where he is within a manageable area which can be watched and controlled."
The Sunday Express said bin Ladin's whereabouts had been discovered from "a combination of CIA paramilitaries and special forces, plus image analysis by geographers and soil experts".
"They studied the background in bin Ladin's last video and matched it to rocks in the Toba Kakar region," the newspaper said.
"A two-man special forces surveillance unit then infiltrated the area," it said, adding they picked up their first clues bin Ladin was in the area within a week.
"Other teams then slipped in," the Sunday Express quoted its source as saying.
"To avoid any alert, helicopters were not used."
A graphic published alongside the Sunday Express report has indicated the area in which bin Ladin is supposedly hiding is to the north of the Pakistani towns of Khanozai and Murgha.