The group is suspected of running much of the insurgency around Kabul and eastern Afghanistan.
But its real power may lie in its connections to Pakistan's spy agency, the Times says.
Pakistani leaders recently offered to broker talks between Afghan President Hamid Karzai and the network.
Many U.S. officials remain skeptical about reconciling the network's senior leaders with the Afghan government, the Times says.
Richard C. Holbrooke, U.S. special representative to Afghanistan and Pakistan, painted a different picture in a briefing Tuesday.
"If they are willing to accept the red lines and come in from the cold, there has to be a place for them," Holbrooke said.
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