A UN team led by German prosecutor Detlev Mehlis is due to report to the Security Council by 25 October on the February assassination which plunged Lebanon into its worst crisis since the 1975-1990 civil war.
The Security Council has already extended the inquiry's original three-month deadline once, but Mehlis now looks set to ask for more time.
"I think [Mehlis] will take all the necessary measures so his mission continues until 15 December, which was the period originally assigned to him by the Security Council," Prime Minister Fouad Saniora told reporters, giving no explanation.
The Security Council ordered the UN investigation after a fact-finding mission concluded Lebanon was incapable of conducting a credible inquiry of its own.
It gave Mehlis three months, but he was allowed to ask for a maximum of three extra months, taking the probe to mid-December.
Al-Hariri was blown up in a truck
bombing in February
It was not clear why Mehlis might need more time, but diplomatic sources have said his team had not ruled out returning to Damascus for more interviews with Syrian officials.
UN investigators last month quizzed several Syrian officials over the assassination of al-Hariri and 20 others in a truck bombing many Lebanese blame on Damascus.
Syria has denied any role in the bombing that killed al-Hariri or an ensuing string of blasts and assassinations that has rocked its smaller neighbour.
A UN official declined to comment on extending the inquiry but diplomatic sources said it was up to the Security Council to decide if Mehlis would get more time.
Several arrests have been made
over the killing
"The decision to extend the mandate is the sole sovereign decision of the Security Council," a diplomatic source said.
"Either way, he must report to the Security Council on 25 October."
Mehlis left Beirut on Sunday, airport sources said, and it was not clear when he would return.
Neither side has named the Syrian officials interviewed by UN investigators but political sources in Lebanon say they include senior intelligence officers working in Lebanon at the time of the blast and their commanders in Damascus.
Lebanon has already arrested four pro-Syrian generals in connection with al-Hariri's killing and charged them with murder.
Their lawyers say they are innocent.
Al-Hariri's killing sparked mass anti-Syrian protests in Beirut that forced Damascus to bow to international pressure and end a 29-year military presence in Lebanon in April.