In an interview, the newspaper said, two of the Taliban's senior Islamic scholars said they have passed on a message from the Quetta shura, the Taliban's ruling council, that Omar wants "sincere and honest talks" with Western leaders.
The newspaper also quotes the scholars as saying Omar no longer seeks to rule Afghanistan.
A senior U.S. military source said the remarks suggested a "breakthrough" was possible. "There is evidence from many intelligence sources the Taliban are ready for some kind of peace process," the source said.
In an interview in Taliban-controlled territory, two leaders of the group said their military campaign sought the return of Islamic law, expulsion of foreigners and restoration of security.
"(Omar) is no longer interested in being involved in politics or government," said Mullah Abdul Rashid, the elder of the two commanders, who used a pseudonym to protect his identity.
"All the mujahedin seek is to expel the foreigners, these invaders, from our country and then to repair the country's constitution. We are not interested in running the country as long as these things are achieved."
He said the Taliban had become too entwined in politics and lacked the ability to govern the country.
The interview came as an American source said U.S. officials were discussing whether President Barack Obama could permit talks with the Taliban.