"I am meeting with President Trump later on and I will tell that, look, there's not going to be a military solution," he told the Council on Foreign Relations before the two leaders' meeting later Monday on the sidelines of the UN General Assembly.
"For 19 years if you have not been able to succeed, you're not going to be able to succeed in another 19 years," Khan said.
Trump has frequently called for an end to America's longest war, launched after the September 11, 2001 attacks, and a senior US diplomat reached a deal to pull troops after a year of negotiating with Taliban militants.
But Trump abruptly ended talks earlier this month, revealing on Twitter that he had invited Taliban leaders to the United States but canceled their visit after a bombing in Kabul killed a US soldier.
Khan -- whose government has sought to use its influence with the Taliban -- admitted that Trump's snapping off diplomacy caught him off-guard.
"We read it in the paper. It should have been at least been discussed with us," he said.
Khan, a former cricket star who has long criticized military operations against extremists, discounted the possibility that the Taliban would topple the internationally recognized government in Kabul without US troops.
"I don't think the Taliban will be able to control the whole country. I think there will be a settlement," he said.
"I honestly believe that this is not the Taliban of 2001. There are lot of things that happened and I believe they will be more accommodating," he said.
The Taliban imposed an austere version of Islam on most of Afghanistan from 1996 to 2001, banning music and girls' education and giving refuge to Al-Qaeda.
Khan also said he would make a new pitch to Trump to mediate on Kashmir, which is divided between Pakistan and India.
Trump a day earlier held a joint rally with Indian Prime Minister Narendra Modi, a Hindu nationalist whose government last month revoked the Muslim-majority region's autonomy and cut off most ordinary people's cellular and internet service.