The Chosun Ilbo newspaper quoted Yoon as saying the joint planning and exercises would be aimed at more effective implementation of the US "extended deterrence."
The term means the ability of the US military, particularly its nuclear forces, to deter attacks on US allies, Reuters reported.
"The nuclear weapons belong to the United States, but planning, information sharing, exercises and training should be jointly conducted by South Korea and the United States," Yoon said, adding Washington is also "quite positive" about the idea.
Yoon's remarks come a day after North Korean state media reported that its leader Kim Jong Un called for developing new intercontinental ballistic missiles (ICBMs) and an "exponential increase" of the country's nuclear arsenal to counter US-led threats amid flaring tension between the rival Koreas.
The North's race to advance its nuclear and missile programmes has renewed debate over South Korea's own nuclear armaments, but Yoon said maintaining the Treaty on the Non-Proliferation of Nuclear Weapons remained important.
At a meeting of the ruling Workers' Party last week, Kim said South Korea has now become the North's "undoubted enemy" and rolled out new military goals.
On Sunday, North Korea fired a short-range ballistic missile off its east coast, in a rare late-night, New Year's Day weapons test, following three ballistic missiles launched on Saturday.
Yoon's comments on the nuclear exercises are the latest demonstration of his tough stance on North Korea. He urged the military to prepare for a war with "overwhelming" capability following North Korean drones crossing into the South last week.
MNA/PR