By Park Si-soo

The United States and North Korea are in "last-minute" negotiations on the agenda for historic talks between Donald Trump and Kim Jong-un, the Chosun Ilbo daily reported on Thursday, citing sources in Washington.

The exact date and venue for the summit could be announced next week, the Seoul-based newspaper said.

Earlier, Trump said the summit would take place "in May or early June."

Chosun reported Trump would demand Kim denuclearize the North over six months or a year after their meeting, citing an unnamed source in Washington. The paper said Trump did not support the idea of a "phased and synchronized" implementation of a denuclearization deal, an option Pyongyang favors.

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Trump does not trust Kim either. So he has pushed forward the idea of "complete, verifiable and irreversible denuclearization."

A source told the newspaper Trump may demand "the denuclearization be done within this year."

Meanwhile, the New York Times reported on Wednesday that the U.S. and the North have been negotiating with "will and sincerity" over the summit details.