World Rugby officials are set to make an announcement at 12pm Japanese time (0300 GMT) on Thursday.
It would be the first time in the tournament's 32-year history that a game has been cancelled. Other possible options include changing venues, officials have said.
France have postponed their team announcement, scheduled for Thursday morning, pending the World Rugby briefing.
Seven games are scheduled for this weekend, the end of the pool stage, but England v France on Saturday in Yokohama is set to be the worst affected by the typhoon on its current trajectory.
Hagibis is ranked as "violent", the highest classification used by the Japanese Meteorological Agency (JMA), and is packing maximum gusts of up to 280 kilometres (174 miles) per hour.
"It is currently a large and violent typhoon. As it moves north and approaches Japan, it will be technically downgraded slightly to a 'very strong' typhoon," said a meteorologist at the Japan Meteorological Agency.
"But the fact remains it will remain very strong when it arrives," he told AFP.
"This is a very large typhoon, which means it may affect significant impact in large areas," he added.
Japan is also hosting its annual Formula One Grand Prix in Suzuka, west of Tokyo, this weekend, with practice sessions starting on Friday. Young driver Jules Bianchi crashed and later died in bad weather conditions caused by a typhoon in 2014.
Typhoon Faxai, which struck Japan about two weeks before the World Cup, caused widespread disruption, leaving two people dead, cutting power supplies and causing more than 100 flights to be cancelled.
Hagibis is currently forecast to clip the southeastern corner of Japan near Tokyo and Yokohama, a similar trajectory to Faxai.
It is expected to weaken considerably as it approaches but Japan is still bracing itself for torrential rain and fierce winds from what forecasters have warned is one of the most powerful storms to hit the country in recent years.
Organisers have touted "robust" contingency plans for every eventuality after deciding to hold the tournament in Japan, subject to around 20 typhoons per year as well as being one of the most seismically active regions on Earth.
Faxai made landfall in Chiba, east of Tokyo, on September 9, causing pandemonium including a lengthy power black-out that affected half-a-million homes.
That storm also had an impact on some teams' arrivals at the Rugby World Cup. England were stranded for hours at Narita Airport, and Australia delayed their arrival from Sydney.
Tournament rules state that a game in the pool phases cannot be rescheduled, as the matches come too thick and fast. Instead they are recorded as a 0-0 draw with both teams given two points.
England and France are already qualified from Pool C, with England top of the group, but Pool A hangs in the balance ahead of Japan's final game against Scotland in Yokohama on Sunday.
If that game were to be abandoned it would be a disaster for the Scots, who would be eliminated, while Japan go through as shock winners of Pool A with Ireland runners-up.
Assuming the All Blacks win their final pool game against Italy, this would set up two delicious quarter-finals.
Ireland, who came into the tournament as the world's leading team, would play New Zealand, the two-time defending champions.
And Japan would set up a repeat of their clash with South Africa, whom they famously beat 34-32 at the last World Cup on the English south coast in a match dubbed the "Miracle of Brighton".