The vessel is believed to have suffered a failure during an exercise and is presumed to have sunk.
The US is said to have been observing the submarine off North Korea’s eastern coast earlier this week and American spy satellites were also later watching the search for it.
“The speculation is that it sank”, an unidentified US official told the US Naval Institute’s news website.
The North Koreans have not made an attempt to indicate there is something wrong or that they require help or some type of assistance.”
The reports emerged as Pyongyang threatened retaliation against US and South Korean forces taking part in annual joint drills.
The North has warned it would launch a “blitzkrieg” in the Korean peninsula amid a simulated amphibious landing by Washington and Seoul involving thousands of .
About 55 US aircraft and 30 US and South Korean ships, including ones which carry attack jets, took part in the assault on beaches near Pohang city in the South.
The North has reportedly warned of a “pre-emptive retaliatory strike at the enemy groups” involved in the exercise which it sees as preparations for an invasion.
Pyongyang said it would respond with an “operation to liberate the whole of South Korea including Seoul” with an “ultra-precision blitzkrieg”.
North Korean state media boasted of the nation’s right to launch a “pre-emptive nuclear attack” and issued a final warning to Washington.
“A nuclear war against the DPRK would bring a final ruin to the US,” said an article in the North’s Rodong Sinmun newspaper.
“This is the last warning of the DPRK to Obama and his cronies in the White House.”
The US and South Korea have defended the drills, saying they are defensive and routine, and are part of eight weeks of joint exercises.