The Pakistan government proposed trading Davis for Siddiqui, an MIT-educated neuroscientist. However, the offer was immediately dismissed by the US administration, ABC News quoted an unnamed senior American administration official and a Pakistani official as saying.
Both officials were involved in negotiations to free Davis. "The Pakistanis have raised it...We are not going to pursue it," the US official said.
The proposal was the latest in a series of efforts to break the impasse between the US and Pakistan over Davis, who was arrested on Jan 27 after he shot and killed two armed men he claimed were trying to rob him.
According to the Pakistani official, the Pakistan's government proposal called for Siddiqui to be transferred to Pakistan, where she would serve the remainder of her sentence in a Pakistani jail or under house arrest.
As per both the US and Pakistani officials, the US government "quickly made it clear to Pakistan that they would not entertain the possibility of trading Siddiqui for Davis".
The American official, who requested anonymity because he was not authorised to speak on the record about the negotiations, said the offer was not being considered by the White House.
The Pakistani official directly involved in the negotiations agreed, saying the proposal was a "non-starter" for the US government.
Davis' case became complicated after the Western media revealed he was a security contractor working for the CIA.Reports have suggested the two men he killed were operatives of the Inter-Services Intelligence agency.
Siddiqui was convicted of trying to shoot FBI agents and military officers in an Afghanistan police station in 2008. She had been arrested the day before after being found with a list of New York city landmarks and instructions on how to construct explosives.
In 2004, FBI director Robert Mueller described Siddiqui as an "Al Qaeda operative and facilitator". The FBI had issued a global alert for Siddiqui and her first husband in 2003 for their suspected ties to Al Qaeda.
Siddiqui later remarried an Al Qaeda operative who was the nephew of 9/11 mastermind Khalid Sheikh Muhammed. Her husband, Ammar al-Baluchi, is currently being detained at Guantanamo Bay.
Siddiqui's case has been raised with the US by Pakistan's top leaders, including Prime Minister Yousuf Raza Gilani, who last year called for Siddiqui's exoneration and release.
Siddiqui was never charged with any terrorism-related crimes. Shortly after the FBI alert, she and her children disappeared, only to surface in Afghanistan five years later.
Siddiqui has claimed she was held in secret American prisons, including Bagram airbase in Afghanistan, but US officials have consistently denied that she was ever in American custody.
US and Pakistani officials told ABC News that the White House had earlier threatened to close the three US consulates in Pakistan and expel the Pakistani ambassador to the US if Davis was not released.
Pakistan''s Ambassador Husain Haqqani has denied that the White House made such threats.
Pakistani officials in Lahore and Islamabad told ABC News that Davis' release is a matter of time and that the Pakistan government is waiting for the public furor over the case to wane before releasing the American.
One Pakistani official said that one likely outcome would be that the US government would pay reparations to the victims'' families, who under Pakistan law can pardon Davis if asked.