It was the first confirmation that Seoul is seeking to postpone the annual Key Resolve and Foal Eagle drills, which usually start in late February or early March and run until the end of April.
But South Korea will host the Winter Olympics in Pyeongchang from February 9 to 25 next year, with the Paralympics scheduled to begin on March 9.
The host area is just 80 kilometres (50 miles) south of the tense border with nuclear-armed North Korea, and tensions tend to rise during the drills, which Pyongyang condemns as rehearsals for invasion.
Moon told US television channel NBC that the two allies were considering postponing the exercises.
"I have made such a proposal to the US and the US is now reviewing it," he said on his way to Pyeongchang to promote the Games.
"However, it will all depend upon how North Korea will behave."
He also expressed hopes the Olympics games will help ease tension running high over the North's relentless nuclear and missile tests.
Games organisers and Seoul are both keen for the North to take part in what they have proclaimed as a "peace Olympics", but the North's participation in sporting events in the South has largely depended on the political and military situation on the Korean peninsula.
Pyongyang has so far given no indication whether it will send its athletes -- two pairs figures skaters have qualified -- to Pyeongchang.
Last month, the South's Unification Minister Cho Myoung-Gyon warned the North Korea could deliver a "fatal blow" to the Olympics if it launches a missile or stages another provocation before the event.
But Moon said: "Foreign tourists coming for the Pyeongchang Winter Games won't need to worry about security. I don't think North Korea will do anything that may undermine the Olympics.
"Everything is now in place and I hope these Olympics will serve as an opportunity to help ease tension with the North", he added.
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