Past visits by senior politicians to Yasukuni -- which honours even convicted war criminals -- have angered China and South Korea.
The conservative Takaichi, who on Saturday became leader of the ruling Liberal Democratic Party (LDP), has visited on many occasions, including as a minister.
However, she is now weighing up the impact on diplomatic ties with Beijing and Seoul, the Yomiuri Shimbun, the Asahi Shimbun and other media reported this week, citing unnamed party sources.
She is also mindful of possible criticism that ally the United States could level ahead of President Donald Trump's expected visit to Tokyo later this month, the Yomiuri newspaper said.
A visit to the shrine in 2013 by then-prime minister Shinzo Abe, Takaichi's mentor, prompted fury from China and South Korea and disquiet from Washington.
The autumn festival, which will be held from October 17 to 19, is a popular time to go to the shrine in Tokyo, including for members of parliament.
Abe's three successors including outgoing premier Shigeru Ishiba stayed away from the site during their terms at the top.
- Social media hostility -
Takaichi, 64, is expected to become Japan's first woman prime minister this month.
Beijing on Saturday reacted to her win by saying "it is hoped that Japan will abide by... its political commitments on major issues such as history and Taiwan, (and) pursue a positive and rational policy toward China".
But on Chinese social media, reaction has been hostile given Takaichi's previous hawkishness on China and previous visits to Yasakuni.
On Weibo, the hashtag "Sanae Takaichi denies the Nanjing Massacre" began trending on October 5 and has since racked up around 97.5 million views.
Japanese troops carried out around six weeks of mass murder, rape and looting in Nanjing from the end of 1937, killing tens if not hundreds of thousands.
Takaichi has not publicly commented on the massacre since becoming LDP leader.
In a 2004 blog, however, she questioned the official Chinese death toll of 300,000 people.
Yasukuni includes a museum that portrays Japan largely as a victim of US aggression in World War II and makes scant reference to Japanese atrocities, including those in Nanjing.
Another hashtag on Weibo, about Takaichi considering not visiting Yasukuni, garnered more than 17 million views.
One post with 31,000 likes said that the Japanese are "terrorists detrimental to world peace".
- Coalition grumbles -
Takaichi's appointment has also unsettled the LDP's coalition partner, the Komeito party, because of her past visits to Yasukuni and historical views, reports said.
Their inability to agree on a renewal of their coalition means that Takaichi's confirmation as premier by parliament has been pushed back, Kyodo News reported.
Originally expected on October 15, it will likely now take place in the week of October 20, Kyodo added.
The LDP-Komeito coalition lost its majority in the upper house in elections in July and in the lower chamber last year.
Other reports this week suggested that Takaichi has approached the Democratic Party for the People (DPP) with a view to it joining the coalition.
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