Although Kan's opponents have only a slim chance of rallying enough support for a successful motion in the Diet legislature, the move would be a fresh headache for the PM, who has been in office for less than a year.
Leaders of the main conservative opposition Liberal Democratic Party (LDP) and its smaller ally the New Komeito party threatened the move on Friday against Kan, Japan's fifth prime minister in as many years.
A rebel powerbroker in Kan's Democratic Party of Japan (DPJ), Ichiro Ozawa, long dubbed the "Shadow Shogun", did not rule out supporting a move to oust Kan, according to an interview published by The Wall Street Journal.
Kan's approval ratings slipped below 20 percent shortly before the March 11 calamity, which sparked the world's worst nuclear crisis since Chernobyl and threw the country back into recession.
A political truce ended about a month after the disaster, and the LDP has rejected Kan's offer for it to join a national unity government.
Ichiro Aisawa, the LDP's Diet affairs chief, told a political talk show on Sunday: "Our party has decided to submit a no-confidence motion against Prime Minister Naoto Kan... It won't be long before we submit it."
He said the LDP's president, Sadakazu Tanigaki, would make the final decision on timing.
The Kyodo news agency said the LDP would submit the motion on Thursday, a day after a debate on quake reconstruction.
Kan has taken some bold steps since the disaster, including shutting down a second quake-prone nuclear plant southwest of Tokyo, the Hamaoka plant, and announcing a radical energy policy review that stresses clean renewables.
But Kan's critics have faulted his handling of disaster relief and the slow pace of building temporary new homes for tens of thousands made homeless by the monster tsunami that hit the northern Pacific coast.
The DPJ's scandal-tainted veteran Ozawa -- who last year narrowly failed in an attempt to oust Kan as party president and premier -- told the Wall Street Journal that he was considering whether to back a move against the premier.
He told the paper he was "thinking about how to deal" with a no-confidence motion and said: "If the prime minister cannot implement policies, it's meaningless for him to stay in power".
"The sooner he is replaced, the better," Ozawa added.
If the motion were passed -- which would require scores of DPJ lower house lawmakers to defect to win a lower house majority -- the premier would have to either resign or call a snap election.
Ozawa, who years ago defected from the LDP, was indicted this year over an alleged violation of campaign-funding laws. He has maintained his innocence.
Asked about his political future, he said: "I'm an old soldier. Have you heard of General MacArthur's words, 'Old soldiers just fade away'? I was thinking about just fading away, but now I feel I have a bit more work to do."
Tomoaki Iwai, a Nihon University politics professor, said for now Kan's opponents would face an uphill battle in pushing through a no-confidence motion. "It will be very difficult," he told AFP.
"More than 80 DPJ members would be needed in order to pass the no-confidence motion against Kan, but I doubt so many people would have resolve that strong.... When Ozawa held a meeting recently with his DPJ supporters, only 60 people gathered."
He also said that the DPJ rebels would have to split away from the party and that this was unlikely because "Ozawa wants to take control of the DPJ".
"For Kan, if the motion is rejected, he would be able to avoid the most immediate crisis and would no longer need to dissolve parliament," said Iwai.
"He would still have to deal with some members who are unhappy about his administration inside the party, but a failed no-confidence motion may actually solidify his political standing somewhat."