Karzai's spokesman could not reached for comment. But the Times, in its report, said the spokesman had confirmed contact had been made and described the past two months as positive.
Officials, however, told the paper the Taliban-initiated talks had been fruitless so far, although they may help explain Karzai's mounting public hostility to Washington.
In November - around the same time the secret talks reportedly began - Karzai announced his intention to avoid signing a bilateral security deal with the United States until after a presidential election in April. Karzai has served two terms and cannot run again.
President Barack Obama, frustrated by Karzai's refusal to sign the accord, was due to meet top commanders at the White House on Tuesday to discuss the future of the U.S. mission in Afghanistan.
Relations have deteriorated sharply over Karzai's refusal to sign, sapping already scant support for the war in Washington, which has halved aid for civilian assistance in the fiscal year 2014.
Washington has signaled it could pull all troops out after 2014, unless a deal is signed soon. This would leave Afghanistan's fledgling security forces to fight the Taliban insurgency alone and diplomats fear they would struggle to cope without U.S. financial and military support.
The Taliban have vowed to derail the April 5 election and the recent spike in violence in the capital suggests secret talks with Karzai have made little difference over their stated intention to step up attacks.
Monthly incidents in January were at the highest since 2008, according to security officials, and the trend has continued into February, with two bombs going off in Kabul on Monday.
(Reporting by Jessica Donati; Editing by Ron Popeski)