Richard Holbrooke, the US special envoy on Afghanistan and Pakistan, told Foreign Policy magazine that Washington was "very pleased" with the selection of de Mistura and looked forward to working with him.
"De Mistura has the unanimous support of the US government," Holbrooke told the magazine's blog The Cable.
But the United Nations denied that Secretary-General Ban Ki-moon had made a decision.
"Any announcement is going to be made by the secretary general. The secretary general has said himself that the selection process is not yet completed," said Martin Nesirky, Ban's spokesman.
The current UN envoy to Afghanistan, Kai Eide of Norway, steps down in March. British Prime Minister Gordon Brown said his successor would be unveiled at a January 28 summit in London on aiding war-weary Afghanistan.
Eide faced criticism from his former deputy, American Peter Galbraith, that he failed to take action to prevent what international observers said was widespread fraud in Afghanistan's election last year.
De Mistura has worked in the world's trouble-spots for more than three decades. He last year ended two years as the UN special envoy to Iraq.
He was personal representative of the UN secretary general for southern Lebanon from 2001 to 2004 and has also served in Somalia, the Balkans and Nepal.
The New York Times in an editorial last week had urged the United Nations to give the job to Jean-Marie Guehenno of France, the former head of the UN peacekeepers.
The newspaper saluted de Mistura's experience but voiced concern that his "low-key style and bureaucratic instincts" were ill-suited to Afghanistan at this critical time.
The New York Times said that Guehenno enjoyed the credibility to stand up to US leaders and Afghan President Hamid Karzai if needed.