Aramco did not give a timeframe or say how much of the company it would sell, but sources have told Reuters the oil company could offer 1%-2% of its shares, raising as much $20 billion-$40 billion.
Some local investors could be selling other shares in order to shift investments to Aramco, in what could be a case of "short-term pain for long-term gain", said Salah Shamma, head of investment, MENA, at Franklin Templeton Emerging Markets Equity.
Saudi Arabia's benchmark index slid 2%, with Al Rajhi Bank losing 1.8% and National Commercial Bank falling 2.5%. The index is down 9% since the start of May.
Saudi British Bank (SABB) fell 4.9% after it posted a flat third-quarter net profit, held back by higher loss provisions related to its merger with Alawwal Bank.
Saudi Basic Industries fell 1.5%.
In Dubai, the index dropped 1.5% as its largest lender Emirates NBD plunged 5% in its biggest intraday fall since Dec. 2018.
In a bourse announcement on Sunday, Dubai Financial Market said that investors purchasing Emirates NBD rights should be aware that in addition to the rights purchase price they need to pay 8.5 dirhams subscription price per share.
The bank on Oct. 17 had approved a capital increase via a rights issue of up to 6.45 billion dirhams ($1.76 billion), lower than the 7.35 billion dirhams that the general assembly had decided on in February.
Blue-chip developer Emaar Properties eased 0.7%, whereas its unit Emaar Malls fell 2.6% after two straight days of gains.
After the close the malls operator reported a rise in third-quarter net profit.
Egypt's blue-chip stock index extended gains for a seventh day, gaining 0.4% as Sidi Kerir Petrochemicals soared 10% and EFG Hermes advanced 2.5%.
Qatar's main index edged up 0.1% led by a 0.9% gain in Industries Qatar and Qatar Fuel was up 1.3%.
The Abu Dhabi index was also up 0.1% with First Abu Dhabi Bank closing 0.4% up.