The Times said that Khalilzad, who has Afghan citizenship, had considered running against Karzai in the country's presidential elections, but missed a May 8 filing deadline.
There are currently 44 presidential candidates registered for Afghanistan's elections, scheduled for August 20.
'Viceroy of Kabul'
The Times report quoted a senior US official as saying that the post would allow the American diplomat to serve as "a prime minister, except not prime minister because he wouldn't be responsible to a parliamentary system".
Siyamak Herawi, Karzai's spokesman, said the report was false.
"We are not aware of this. We cannot confirm this. There is no truth in it," he said.
The chief executive idea was proposed by Gordon Brown, the British prime minister, the paper's sources said.
They also said that Karzai had sought out Khalilzad, who holds no position in the current US administration.
US and British officials have expressed concern that a belief that the West was behind the plan could hamper efforts in Afghanistan, where US and Nato forces have been fighting the Taliban since they pushed them from power in 2001.
As the US ambassador in Afghanistan from 2003-05, Khalilzad played an unusually hands-on role in Afghan politics - Afghans even referred to him as the "Viceroy of Kabul".