The Pentagon sent the naval group from Singapore toward North Korea earlier in April amid tensions on the Korean Peninsula. US President Donald Trump said an "armada" has been sent, but the date and time of the drill remains unknown.
The armada's current location is unknown.
US Vice President Mike Pence said on Saturday that the Carl Vinson would arrive "within days" with no further details provided.
"Our revolutionary forces are combat-ready to sink a U.S. nuclear-powered aircraft carrier with a single strike," the Rodong Sinmun newspaper said as quoted by Reuters.
The North Korean newspaper called the aircraft carrier a "gross animal" and claimed a strike on it would be "an actual example to show our military's force".
Tensions on the Korean peninsula have risen in the wake of Pyongyang's nuclear tests and ballistic missile launches conducted in violation of the UN Security Council's resolutions.
North Korea reportedly carried out the most recent missile test early on Sunday. However, the launch was unsuccessful, according to South Korean defense officials. The North Korean Foreign Ministry said that the alleged missile launch had not been announced officially, though it's Pyongyang's "sovereign right" to conduct such tests.