Khan, who was in the middle of a three-day U.S. visit Tuesday, has repeatedly said the men, an American and Australian, could be freed from the Taliban-linked militants who have held them for nearly three years.
"We will be giving you good news about the two hostages," Khan told President Donald Trump in their meeting Monday at the White House.
The prime minister did not mention them by name at the White House but in a later interview said he was referring to an American and an Australian kidnapped by the Taliban.
"Pakistan is playing its part," he told Fox News with Brett Baier. "And I think we're very close. We hope to give some good news in the next 48 hours."
In its ongoing negotiations with the Taliban, the U.S. has been pressing for the release of American Kevin King, 62, and Australian Timothy John Weeks, 50, of Sydney. It's unknown where King grew up in the United States, but the FBI said he speaks both English and Thai.
The men, both English teachers at the American University of Kabul, were abducted August 2016 as they returned to the campus in the Afghan capital.
The following January, the Taliban released a video in which the two professors asked Trump, who was then president-elect, to offer to exchange prisoners with the militants for their release.
In October 2017, Taliban spokesman Zabihullah Mujahid released a statement saying King was suffering from heart and kidney problems, and often loses consciousness. Mujahid said the Taliban would hold the U.S. government responsible if anything happened to King.
It is widely believed the two Westerners have been held by the Haqqani group, which has close ties to Pakistan's premier intelligence agency known as the ISI. In exchange for the two professors, the Haqqani group has long demanded the release of Anas Haqqani, a brother of Sirajuddin Haqqani, who was captured by Afghan intelligence agents in 2014.
The Haqqani network also held Sgt. Bowe Bergdahl, a U.S. soldier who was freed in 2014 in exchange for five Taliban prisoners who were held at the U.S. military prison at Guantánamo Bay, Cuba.
Trump told reporters before his meeting Monday with Khan that they would discuss hostages. Also missing is American Paul Overby, an author in his 70s who had traveled to the region several times but disappeared in eastern Afghanistan in mid-2014.
The U.S. is seeking the release of Dr. Shakil Afridi, a doctor who ran a fake vaccination campaign to help the U.S. confirm the whereabouts of Osama bin Laden before the May 2011 U.S. raid on his compound. The doctor is being held in a Pakistani prison.
Khan told Fox that Pakistan might consider swapping Afridi for Pakistani neuroscientist Aafia Siddiqui, who was sentenced in 2010 in U.S. federal court in New York to 86 years in prison for assaulting and trying to kill Americans serving in Afghanistan. She is being held at the Federal Medical Center Carswell in Fort Worth, Texas.
"Yes, we could negotiate some sort of swap," Khan told Fox.
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