Army Sergeant Bowe Bergdahl. PHOTO: AFP
The move is an attempt to free Army Sergeant Bowe Bergdahl before the majority of US forces leave Afghanistan by the end of 2014, the report said, citing current and former officials.
The swap would trade Bergdahl for five Taliban members who would be released from Guantanamo Bay into protective custody in Qatar, the Post reported.
State Department spokeswoman Jen Psaki told AFP that she could not discuss details of US efforts but that "there should be no doubt that we work every day - using our military, intelligence and diplomatic tools - to try to see Sergeant Bergdahl returned home safely."
According to the Post, the offer has not been formally made, adding that Bergdahl is thought to be held in Pakistan by the Haqqani network.
The US Army sergeant is the only American soldier held captive by Taliban militants.
In January the United States obtained a "proof of life" video of Bergdahl - the first providing evidence he was still alive in more than three years.
Bergdahl disappeared in June 2009 from a base in Afghanistan's eastern Paktika province, with the Taliban later saying they had captured him.
US officials had previously considered a possible swap in which Bergdahl would be let go in exchange for the release of Taliban members held at Guantanamo Bay, but the deal was never clinched.
The US-led Nato military mission in Afghanistan is due to end this year. But negotiations between Kabul and Washington could mean that about 10,000 US troops stay in Afghanistan after 2014 on training and counter-terrorism operations.
The deal to allow the residual US force, however, has been the subject of months of bitter public wrangling between President Hamid Karzai and US officials.
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