Saudi Aramco said that Goldman Sachs may stabilize its shares after a record IPO earlier this month.
Stabilization agents support the share price by purchasing additional shares on the market.
The stabilization period will end on January 9, but so far no transactions have been executed, it said in a statement.
Aramco shares ended nearly 0.6% lower at SAR35.40 ($9.44). This is above its IPO price of SAR32 per share, valuing the oil giant at about $1.9tn.
The shares have eased after hitting an intraday high of SAR38.7 on December 12.
The offering process, which concluded on 4th December, generated subscriptions by institutional and individual subscribers of SAR446bn (US$119bn), or 4.65 times the total offer shares.
The offering attracted more than five million subscribers.