BEIJING—The head of the Roman Catholic Church in Hong Kong signaled that the Vatican and Beijing are nearing an accord over how Chinese bishops are picked, a key step toward “normalizing” bilateral ties marred by six decades of estrangement.

In a recent essay, Cardinal John Tong didn’t give details of the proposed deal, but expressed optimism that Rome wouldn’t compromise on religious principles in trying to resolve disputes over China’s insistence on having a state-controlled body appoint local bishops.

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