Saudi Aramco shares were indicated at 35.2 riyal ($9.39) each in the pre-market auction on Wednesday, 10% above their IPO price of 32 riyals, Refintiv data shows.
Saudi Arabian Oil Co (Aramco), whose shares make their stock market debut at 0730 GMT, priced its record initial public offering (IPO) last week, raising $25.6 billion.
The flotation valued the world's most profitable company at $1.7 trillion. A 10% increase in the share price would take its market capitalisation closer to the $2 trillion price tag long sought by Saudi Crown Prince Mohammed bin Salman.
Saudi Arabia relied on mainly domestic and regional investors to buy a 1.5% stake in Aramco after lukewarm interest from abroad.
The $25.6 billion of proceeds beat Chinese tech firm Alibaba's $25 billion listing in 2014.