If confirmed, the supposed agreement between Cardinal Jean-Louis Tauran and Mohammed bin Abdel Karim Al-Issa of the Muslim World League would mark a historic first in Saudi history.
The cardinal has visited Saudi Arabia this year and met the royal family, urging the Muslim country to treat its citizens equally.
Under the alleged agreement the churches will be built alongside the establishment of a committee to improve relations between the two, Egypt Independent reports.
There was no immediate confirmation from the Vatican. MailOnline has approached Vatican and Saudi authorities for comment.
Saudi Arabia's anti-extremism Etidal centre hosted Cardinal Tauran last month as the crown prince pushes for inter-religious exchange in the ultra-conservative Sunni kingdom.
There are no Christian churches in Saudi Arabia, the only country in the region without one.
The Vatican has previously spoken of its wish to provide the Christian population of Saudi Arabia with the ability to worship.
During the visit earlier this year Riyadh-based Etidal, the Arabic acronym for the Global Center for Combating Extremist Ideology, discussed with the cardinal its use of media and technology to 'disrupt extremist recruitment and promote tolerance', a government statement said.
'I think we have two enemies: extremism and ignorance,' Tauran was quoted as saying in the statement, while lauding the centre that was established in 2017.
'I don't believe in the clash of civilisation but rather in the clash of ignorance. Most of the time people react because they don't know who you are or who they are.'
Tauran, seen as an energetic promoter of dialogue between the Roman Catholic Church and Islam, also met Saudi King Salman in the capital.
Saudi leaders have courted a flurry of representatives of various Christian traditions in recent months.
In November, the head of Lebanon's Maronite church, Beshara Rai, met King Salman and powerful Crown Prince Mohammed bin Salman in a historic visit to Riyadh.
The prince also reportedly met a group of Jewish and Catholic leaders in a recent visit to New York, which highlighted a rare show of interfaith dialogue.
Prince Mohammed, the heir to the Saudi throne, has sought to project a moderate image of his austere kingdom, often associated in the West with jihadist ideology and subjugating women.
The reformist prince has announced the lifting of a ban on women driving and has authorised cinemas for the first time in over three decades as part of his pledge to spread a more moderate version of Islam.
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