In a telephone conversation with Prime Minister Shinzo Abe on December 12, Biden repeatedly urged the Japanese premier to stay away from the shrine, Kyodo News said, quoting unnamed diplomatic sources.
Yasukuni is a memorial to around 2.5 million war dead, but is controversial because those commemorated include a number of senior figures condemned to death at the end of World War II for their role in directing the conflict.
Immediate confirmation of the report was not available.
Abe's December 26 trip to the shrine drew condemnation from China and South Korea, who view visits there as a symbol of what they say is Japan's unwillingness to come to terms with its wartime aggression.
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The shrine is also controversial because of an attached museum that offers a narrative of the war most historians find unacceptable, and which presents Japan as a frustrated liberator and a victim, rather than an aggressor.
US diplomats privately acknowledge they were surprised by the move and say they had made their opinions known to the prime minister's office in advance.
But the news that personal overtures from Joe Biden, who has enjoyed a good working relationship with senior Japanese figures, were rejected will be an embarrassment to the White House.
Abe has defended his visit to Yasukuni as "natural" and said he had no intention of hurting the feelings of Chinese or Koreans.
The Japanese prime minister has not held a summit with Chinese president Xi Jinping or South Korean President Park Geun-Hye since taking office in December 2012, with Tokyo locked in separate sovereignty disputes with its neighbours.