The wedding led to a threat of excommunication
But representatives of the couple may not be able to agree on conditions for the meeting.
Zambian Archbishop Emmanuel Milingo, 71, has been on a "spiritual retreat" for the past two weeks, according to the Vatican, prompting his wife to begin a hunger strike until she sees him again.
But the Vatican statement reporting Mr Milingo's offer to see Mrs Sung said "the Holy See cannot and will not impose on the conscience of the Archbishop".
Excommunication threat
The Vatican threatened Mr Milingo with excommunication after his marriage in New York in May, conducted by the group popularly known as the Moonies.
It dropped the threat after he returned to the Vatican and reportedly swore loyalty to the Pope. He has not been seen in public since a private meeting with the pontiff in early August.
A Vatican statement sent to Mrs Sung, 43, on Wednesday said Mr Milingo was willing to meet with her "to communicate his decision".
But she demands that the two be allowed to meet alone, a condition the Vatican has been unwilling to accept.
"Maria has been fasting for one purpose - for a private meeting with her husband. Nothing else can be discussed," said her spokesman, the Unification Church's Reverend Phillip Schanker.
He said that five other conditions set by the Vatican were acceptable, but did not say what the terms were.
Mediation effort
The South Korean Ambassador to the Vatican has been trying to mediate in the dispute, but has not succeeded in bridging differences.
Mrs Sung at one point suggested she might be pregnant with the archbishop's child, but tests last week showed she is not.
Archbishop Milingo has long been a problem for the Holy See.
In an almost unprecedented move, the Vatican essentially removed him from his post in Zambia in the early 1980s and brought him to Rome.
Last year, it issued new rules on excommunication that were widely seen as an effort to control his popular faith healing sessions.