The details of the extraordinary "deal" emerged after a confidential American briefing was found at bin Laden's hide-out in Pakistan's garrison town of Abbottabad, the Sunday Mirror reported.
According to the paper, reports in Pakistan claim that Baradar co-founder of the Taliban and one of bin Laden's most trusted allies, is named in the papers.
He and other "moles" within bin Laden's organisation are said to be feeding crucial information to US intelligence experts, the paper said.
Until now it has been believed that bin Laden was caught out when the US intercepted a phone call made by his courier Abu Ahmed al-Kuwaiti, who was also killed in the covert US raid on May 2.
But new reports in Pakistan suggest it was actually Baradar who told the US where he was hiding, the paper said.
Baradar, known as the "father of the IED" because he pioneered the use of roadside bombs in Afghanistan, was arrested in a joint Pak-US operation last year in Karachi and was interrogated in prison before being released last October.
Mullah Baradar, in his early 40s, is the deputy of Taliban chief Mullah Mohammed Omar and the leader of the militant Quetta Shura in Pakistan.
"The US has announced that it is scaling back its military operations in Pakistan following the killing of bin Laden. That will fuel speculation about whether this is the start of the pay-off for insurgents who are willing to cut a deal," the paper quoted security expert Neil Doyle as saying.