An appeal against Saddam's conviction, for the 1982 killing of 148 people in Dujail, failed on Tuesday. The court upheld the original ruling that the former Iraqi president should be hanged within 30 days.
If presidential approval is not required, Saddam would lose his last legal means of avoiding the death penalty.
Iraqi officials had said prior to the appeal court ruling on Tuesday that any decision to impose the death penalty must be ratified by Talabani and Iraq's two vice-presidents.
But lawyers were debating whether an Iraqi high tribunal provision mandating imposition of the death penalty could take precedence over a law in the constitution that requires the president to approve death sentences.
Meanwhile, the Baath party, formerly led by Saddam, threatened that it would target US interests anywhere if he is executed.
The statement appeared on Wednesday on a website known to represent the party, which was disbanded after US-led forces overthrew Saddam in 2003.
The site is believed to be run from Yemen, where several Baath party members are in exile.
"Our party warns again of the consequences of executing Mr President and his comrades," the statement said.
"The Baath and the resistance are determined to retaliate, with all means and everywhere, to harm America and its interests if it commits this crime," the statement said.
"The American administration will be held responsible for any harm inflicted on the president because the United States is the decision-maker [in Iraq] and not the puppet Iraqi government."
Meanwhile, three Iraqi soldiers were killed on Wednesday when a roadside bomb exploded alongside their patrol in the south of the country.
The soldiers, from the 8th Division of the 3rd Brigade, were killed when the device exploded on the road between Suwaira and Jabala, northwest of Kut, said the military source.
Mamun Agil, a medical official at Kut hospital, confirmed the deaths and said two more soldiers had been wounded in the attack.
Iraq's US-backed security forces are subject to daily attack from fighters battling for supremacy following the 2003 US-led invasion.