How sick is Kakuei Tanaka, Japan's former prime minister? The Japanese press and those who would like to replace him as the overlord of Japanese politics have been trying to find out ever since he suffered a stroke almost three months ago.

The web of mystery spun by the family and personal staff around the 67-year-old Tanaka, who seems to continue to wield great political power even from his sickbed, rivals the best the Kremlin can do in keeping secret a high-level illness. Lately, deception and outright lies have been used to hide where Tanaka is.

It reached the point earlier this month where Prime Minister Yasuhiro Nakasone had to issue an official statement to put to rest a report that Tanaka was dead.

By current reports, Tanaka is alive and sequestered at his home in Tokyo's Mejiro district. The right side of his body is said to be paralyzed and his speech impaired.

The former prime minister commands the largest of five major factions in the Liberal Democratic Party, that has dominated Japanese politics for decades.

Tanaka, a tough-talking man who rose to the prime ministership with only a high school education, was convicted in 1983 of accepting a $2 million bribe from the Lockheed Corp. and was sentenced to four years in prison. But he refused to resign his seat in parliament pending an appeal and set off a train of events that led to new lower house elections. Tanaka retained his mandate, receiving more votes than any other candidate and ignored demands that he quit politics.

Tanaka's standing is especially important for Nakasone, who won office in 1982 and again last year because Tanaka put his faction behind him. If Tanaka left the scene, the faction could turn against Nakasone.

Doctors originally predicted Tanaka would be out of circulation for three to four weeks. They later extended it to two to three months. As Tanaka failed to appear publicly, issue written statements or allow a bedside photo to be taken, speculation mounted that his condition was so bad he would never recover.

The news media staked out the hospital. But on May 5, a Tokyo newspaper weighed in with a big scoop. Tanaka was no longer at the hospital, it said, but had been secretly driven home seven days earlier.

Tanaka's daughter Makiko had been calling there frequently. Bodyguards provided by the Tokyo police were still outside his room. And just the day before, on Tanaka's 67th birthday, his staff had told reporters that the boss had celebrated with a cake in his room.

That day, Tanaka's personal secretary, Shigezo Hayasaka, told reporters that the former prime minister had asked to be taken home and the request was granted. But now Tanaka was back in the hospital receiving therapy, he said. Hospital director Tsunehiko Watanabe gave a similar account. Six days later, both men offered apologies at a press conference, saying they had lied about Tanaka's return to the hospital. In fact, Hayasaka said, Tanaka was still at home, attended by three therapists. There was no further explanation.

Confusion mounted as Makiko Tanaka, who is married to a politician in her father's faction, issued a statement that she had cut off talks with Hayasaka and the hospital about her father's future.

Still, more confusion was created when a businessman visited Tanaka's home and told reporters that he had seen Tanaka. Later he said he had not seen Tanaka and only made his statement to get rid of reporters.

There is no end to speculation now. By some accounts, Tanaka's return home proves he is recovering. By others, it proves he is incapacitated and under control of Makiko, who is now being jokingly named as a successor. By still other interpretations, Tanaka had come home to prepare for death.

Meanwhile, rivals are preparing for the succession as faction leader. Attention has focused on Noboru Takeshita, finance minister in the Nakasone Cabinet and acknowledged prince of the Tanaka faction. Other speculation has focused on the ruling party's vice president Susumu Nikaido, a Tanaka faction member who briefly revolted against Tanaka last fall and considered challenging Nakasone in a party election.