The state-owned oil giant is marketing a USA dollar-denominated debt issue split into six tranches with maturities ranging from three to 30 years.
Speaking at an event in Riyadh, Falih said the issue, which was announced last week, will close on Wednesday and that he believed demand for the bond was "north of" $30bn.
The Aramco deal is one of the most hotly anticipated debt deals of the year, marking the first time the Saudi oil giant has tapped the global bond market.
Saudi Arabia's Energy Minister Khalid al-Falih said on Monday that the bond issue to raise $10 billion towards Aramco's purchase of a controlling stake in chemicals behemoth SABIC was already over-subscribed by three times. Kitco Metals Inc. and the author of this article do not accept culpability for losses and/ or damages arising from the use of this publication.
Aramco is selling the debt in five parts, with the longest maturity, a 30-year bond, to yield 155 basis points over U.S. Treasuries, the people said, asking not to be identified as the details are private.
Neither banks nor investors appear to have been deterred from participating in the high-profile deal, despite initial displays of outrage from companies such as JPMorgan over the death of Khashoggi in the Saudi consulate in Istanbul.
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"As the world's most profitable company, it can be argued that Aramco does not need to resort to debt offering and that the bond serves a secondary goal to inspire confidence and offer new transparency into Aramco's finances, as the company fires up its global expansion strategy", said Anna Belova, senior oil and gas analyst at GlobalData.
Aramco, however, said the bond issue was not linked to the SABIC acquisition and many see it as a relationship building exercise with worldwide investors ahead of its planned initial public offering, scheduled for previous year and then postponed to 2021.
"We assume the transaction will be funded largely from Saudi Aramco's free cash flows, and the company's leverage will remain very conservative by industry standards", the ratings agency said.
Aramco's first foray into worldwide debt markets had previously been expected to raise around $10 billion, to be put toward the cost of acquiring the Saudi industrial conglomerate SABIC, valued at almost $70 billion.
The issue follows on the heels of Aramco's planned $69.1bn acquisition of a 70 per cent stake in petrochemicals company Sabic from the Saudi sovereign wealth fund. Aramco, however, said the bond issue was not linked to the Sabic deal.
"Oil majors are more advanced in their efforts to further vertical integration, but national oil companies are catching up", Fitch Ratings wrote in a comment on the SABIC acquisition.