The Vatican is holding talks with Saudi Arabia on building the first church in the kingdom, where some 1.5m Christians are not allowed to worship publicly.
Archbishop Hashem discussed the Saudi talks whilst visiting Qatar
Archbishop Paul-Mounged el-Hachem, one of Pope Benedict XVI's most senior Middle East representatives, said the discussions had begun a few weeks ago.
But the archbishop cautioned that the Vatican could not predict the outcome.
The discussions come in the wake of King Abdullah's historic meeting with the Pope at the Vatican last November.
A Catholic-Muslim Forum was also set up by the Pope two weeks ago to repair relations between the two faiths after the crisis caused by a speech he gave in Germany in 2006, in which he appeared to associate Islam with violence.
The disclosure of talks between the Vatican and Saudi Arabia, which do not have diplomatic ties, came soon after the first Roman Catholic church in the Qatari capital, Doha, was opened in a service attended by 15,000 people.
Archbishop Hachem, the Apostolic Nuncio to Kuwait, Qatar, Yemen, Bahrain and the UAE, who attended the inauguration, said he hoped there would soon be a similar church for the many Christians in neighbouring Saudi Arabia.
"Discussions are under way to allow the construction of churches in the kingdom," he said.
Although he made clear the outcome was uncertain, the archbishop added that a church in Saudi Arabia would be an important sign of "reciprocity" between Muslims and Christians.
The Vatican has noted that Muslims are free to worship openly in Europe and demands religious freedom as a condition for the opening of diplomatic relations.
About a million Catholics, many of them migrant workers from the Philippines, live in Saudi Arabia.
They are allowed to worship in private, mostly in people's homes, but worship in public places and outward signs of faith, such as crucifixes, are forbidden.
The last Christian priest was expelled from the kingdom in 1985.
Christians complain that rules are not clear and that the Saudi religious authorities, who enforce the kingdom's conservative brand of Islam, Wahhabism, sometimes crack down on legitimate congregations.
The authorities cite a tradition of the Prophet Muhammad that only Islam can be practised in the Arabian Peninsula.
A spokesman for Pope Benedict, Father Federico Lombardi, said: "If we manage to obtain authorisation for the construction of the first church, it will be an outcome of historic dimensions."