A second source confirmed the approach to ADIA, while two other sources said GIC had been approached.
All the sources who spoke to Reuters asked to be anonymous as they were not authorised to speak to the media.
Abu Dhabi's state investor Mubadala Investment Co, which has $229 billion under management, has also been approached by Aramco's advisers, two sources said.
One of the sources said the approaches were still at an early stage and some of the funds had yet to study the proposals before deciding whether to invest.
Among Gulf investors, Bahrain's sovereign wealth fund Mumtalakat was expected to consider investing in the IPO, another source said.
ADIA and Mubadala declined to comment, while Aramco and Mumtalakat did not immediately respond to a request for comment.
The approaches to sovereign funds in countries on friendly terms with Saudi Arabia and wealthy Saudi families indicate bankers aimed to build an investor base to achieve the $2 trillion valuation targeted by Crown Prince Mohammed bin Salman.
The listing is the centrepiece of the crown prince's plan to shake up the Saudi economy and diversify away from oil.
The talks show work on the IPO process is still proceeding despite uncertainty over the timeline following a Sept. 14 attack on Aramco's facilities.
To achieve the $2 trillion valuation, Aramco needs the initial listing of a 1% stake on the Saudi market to raise at least $20 billion. To beat the record for the world's biggest IPO, it needs to top Alibaba's sale of $25 billion of shares.
But bankers and company insiders have described the valuation as ambitious, due to a weak outlook for oil prices as deepening climate change activism could dampen investor interest, particularly in the Western world.
A further risk to the $2 trillion target was raised by the Sept. 14 strikes that knocked out more than half the production of the world's top oil exporting nation. Saudi Arabia has been assuring investors it can quickly restore output.
Various sources said the kingdom has been busy looking for a more sympathetic investor base in the Middle East and Asia, while also seeking support from the wealthiest Saudi families.
"It is a natural fit and many in the region would look at it favourably as they want a piece of the pie," a Gulf source said.
Preparations for the IPO have gone through various stages since the 2016 announcement.
Issues of governance and disclosure, the acquisition of a 70% stake in petrochemicals maker Saudi Basic Industries Corp, disagreements among Saudi officials and advisers over the choice of an international listing venue, all contributed to a temporary halt last year.
Bankers from around 20 international and domestic financial institutions are now working on the company's plan to sell 1% in Riyadh before an international sale in 2020 or 2021.
After securing support from sovereign funds, bankers would focus on Western institutional investors, another source said.
"There's no turning back now," one of the sources said, adding that Aramco was "going ahead" with the IPO.
One of the sources said Aramco could announce its intention to float on Oct. 20, with analysts' reports expected the same day. Analysts have been holding meetings at Aramco's headquarters in Dhahran this week.
(Reporting by Clara Denina, Saeed Azhar, Anshuman Daga and Stanley Carvalho; Additional reporting by Ghaida Ghantous, Hadeel Al Sayegh and Dahlia Nehme in Dubai; Editing by Edmund Blair) ((firstname.lastname@example.org)(+44 207 542 9420)(Reuters Messaging: email@example.com)(Twitter: @claradenina))