The world's top oil company will announce its intention to float (ITF) on November 3, the sources added.
"The Crown Prince finally gave the green light," said one source.
However, Aramco declined to comment.
Saudi Aramco officials and advisers have been meeting with investors at the last minute in an effort to reach as close to $ 2 trillion as possible ahead of an expected listing on Sunday, according to sources.
The final meeting of the Saudi government on Friday night was to decide whether to proceed with the listing.
Although Crown Prince Mohammed put a value of $ 2 trillion on the company in early 201
At that price, Aramco will still be worth at least 50% more than the world's most valuable companies, Microsoft and Apple, each with a market value of around a billion dollars.
Riyadh wants to list a 1% -2% stake in the Saudi stock market to raise at least $ 20 billion and $ 40 billion.
If the deal exceeds $ 25 billion, Aramco will become the largest stock exchange listing in the world, topping Alibaba's $ 25 billion stock exchange listing in 2014.
The entry is the centerpiece of the Crown Prince's plan to shake up the Saudi economy and diversify from oil. But there have been various delays since it was announced in 2016.
Prince Mohammed finally wants to list as much as 5% of the company. International sales are expected to follow the domestic stock exchange listing.
The analyst meetings with the best institutional investors are likely to begin on Sunday, another source said.
The state-owned oil major has also approached governments in the Gulf and Asia, including China, to try to secure the majority of land investment on friendly terms with Saudi Arabia, as the reception has been cooler elsewhere, sources have previously said.