The Argentina Football Association, which hosts the South American championship July, has asked Japan to reconsider its decision to pull-out of the event, Japan Football Association (JFA) vice president Kozo Tashima said.
"The Japanese association for its part has not reached a final conclusion," he said, according to the Jiji Press news agency and other media.
"We will reconsider whether we can send a national team by using our wisdom more than ever."
JFA president Junji Ogura told South American Football Confederation president Nicolas Leoz on Monday that the Asian champions cannot take part in the tournament, where they were invited as guests along with Mexico.
The nation's J-League has suspended its season for five rounds until 23 April to save the electricity used during night matches, planning instead to play the postponed matches in July.
The month has been originally set as a summer break to free up players for the Copa America, prompting Japan's withdrawal.
But Argentina Football Association president Julio Grondona met with Ogura on Tuesday and urged Japan to rethink their decision, according to Tashima.
"They wanted to position the South American championship as an event to support Japan's reconstruction," he said.
"It won't be easy to reach a conclusion. We could either withdraw or go," Tashima said, adding that his association has until April 15 to make a final decision.
The 9.0-magnitude quake and tsunami devastated Japan's Pacific coast and crippled a nuclear power plant, also caused wide-ranging electricity cuts and heavy disruption to football, baseball and other sporting events.