The unknown class of vessel had been reportedly operating off the North Korean coast earlier in the week when it disappeared.
A South Korean defence ministry said Seoul was investigating the reports. Pentagon officials declined to comment on the matter.
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American spy satellites, aircraft and ships have been watching as the North Korean navy searched for the missing sub, the report added.
The US is unsure if the missing vessel is adrift or whether it has sunk, CNN reported, but officials believe it suffered a failure during an exercise.
The US Naval Institute (USNI) News said the submarine was presumed sunk.
"The speculation is that it sank", an unidentified US official was quoted as telling the USNI News.
"The North Koreans have not made an attempt to indicate there is something wrong or that they require help or some type of assistance, " he added.
The incident comes as tensions were further heightened on the Korean peninsular by a fresh threat from Pyongyang.
The official KCNA news agency, citing a statement from military chiefs, warned of a "pre-emptive retaliatory strike at the enemy groups" involved in the joint US-South Korean drill.
Pyongyang added it planned to respond to the drills with an "operation to liberate the whole of South Korea including Seoul" with an "ultra-precision blitzkrieg".
Responding to the statement, South Korea's defence ministry urged Pyongyang to stop making threats or further provocations, according to Yonhap news agency.
North Korea's navy operates a fleet of some 70 submarines, most of them being rusting diesel submarines that are capable of little more than coastal defence and limited offensive capabilities.
But the old, low-tech submarines still pose substantial threats to South Korean vessels.
In 2010, a South Korean corvette was reportedly torpedoed by a North Korean submarine near their sea border.
In August last year, Seoul said said 70% of the North's total submarine fleet -- or around 50 vessels -- had left their bases and disappeared from South's military radar, sparking alarm.
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