Zain Saudi's $1.6bn rights issue, which closes on Tuesday, has so far sold only 54 percent of shares available, the lead manager said on Monday.
Parent telecom operator Zain and underwriting banks are set to meet any shortfall.
That could potentially raise Zain's shareholding in Saudi Arabia's No.3 operator to above 50 percent from 25 percent at present, forcing the Kuwaiti firm to consolidate loss-making Zain Saudi's earnings onto its balance sheet.
Lead manager Saudi Fransi Capital, a unit of Bank Saudi Fransi, and Rajhi Capital, part of Al-Rajhi Bank , have each underwritten 44.8 percent of the issue's 600 million shares, with three other banks covering the remainder.
Under Saudi market regulations, all rights issues must be fully underwritten by banks.
But Zain's chairman said in March that his firm would guarantee the issue, which appeared to suggest that it might end up buying all shares left unsold in the offer.
The shares are priced at 10 riyals each, potentially raising SR6bn ($1.6bn), with the issue open from July 10-17.
With one day left until it closes, Zain Saudi has sold 325 million shares, according to Saudi Fransi Capital.
Of the shares sold, 254.6 million - worth SR2.55bn - were allocated through converting loans from founding shareholders into equity.
These loans totalled SR4.07bn as of March 31, with SR2.5bn provided by Zain, and it is unclear whether these loans were converted on a pro rata basis.
If this was the case and Zain also ended up buying the 46 percent of unsold shares from the rights issue, its shareholding would increase to about 51 percent, according to Reuters calculations.
Saudi market rules do not prevent majority foreign ownership of a Riyadh-listed company, said Amine Bentaleb, director of asset management at Arqaam Capital in Dubai.
Prior to the rights issue, Zain Saudi also cut its capital earlier this month to SR4.8bn from SR14bn to alleviate accumulated losses, which topped SR10bn at the end of March.
Zain Saudi's shares fell 4.4 percent on the Riyadh bourse, ending at all-time low of 11.90 riyals, with some traders opting to sell the shares and buy into the lower-priced rights issue.For all the latest business news from the UAE and Gulf countries, follow us on Twitter and Linkedin, like us on Facebook and subscribe to our YouTube page, which is updated daily.