The ship, which has been ablaze for almost a week since it collided with another vessel on Saturday night in the East China Sea, was about 300 km northwest of Sokkozaki on the island of Amami Oshima as of Thursday afternoon, a spokesman from the Coast Guard's 10th region based in Kagoshima said.
Amami Oshima is one of the northern islands in the Ryukyu islands chain that includes Okinawa.
The tanker Sanchi, owned by Iran's top oil shipping operator National Iranian Tanker Co, was carrying almost 1 million barrels of condensate, an ultra-light, highly flammable crude oil, to South Korea.
It collided with the freighter CF Crystal that was carrying grain from the United States about 160 nautical miles off China's coast near Shanghai.
The spokesman said that Chinese authorities turned down an offer from the Japanese Coast Guard to help, saying it would ask for help when needed.
He said it was not clear if the tanker would drift into Japan's territorial waters, which are about 280 km away.
The Coast Guard has sent patrol boats and aircraft to get the latest information about the tanker and is monitoring the situation, he said.
The Sanchi had a crew of 32 sailors at the time of the collision. The body of a mariner suspected to be from the ship was recovered on Monday and sent to Shanghai for identification. The rest of the crew, which included 30 Iranians and two Bangladeshis, remains missing.
(Reporting by Yuka Obayashi in TOKYO; Writing by Josephine Mason in BEIJING; Editing by Christian Schmollinger)