Trump's approval to kill him was given seven months ago, "if Iran's increased aggression resulted in the death of an American," NBC TV network reported on Monday quoting five anonymous sources.
But the network said that according to the unnamed current and former officials, "The presidential directive in June came with the condition that Trump would have final sign-off on any specific operation to kill Soleimani."
If true, it would bring into question Trump's claim that he ordered the killing only because Soleimani had threatened US diplomatic missions, adding ammunition to his critics who oppose the US President's action.
Soleimani, an Iranian Major General, was killed in the attack near the Baghdad airport on January 3.
The killing of an American contractor in Iraq by militias allied with the Iranian Quds Force that Soleimani commanded was the immediate cause that precipitated his killing, Trump initially said.
But muddling the picture, Trump told Fox News on Friday that "probably" four embassies in the Middle East were in Soleimani's crosshairs when he ordered his killing.
Further adding to the controversy, Defence Secretary Mark Esper said on Sunday in CBS talk show that he did not see intelligence specifically about four embassies, but shared Trump's view that Iran or militias affiliated with them were going after US missions.
The Trump-ordered killing of Soleimani put the world on edge when Iran retaliated directly with rocket attacks on military bases with US troops in Iraq.
But both Trump and Iran backed off escalating the confrontation that could have spiralled into war.
The Democrat-controlled House of Representatives passed a resolution on Thursday aiming to prevent Trump from going to war.
The resolution is not legally binding as it does not have the authority of a law.
Trump's action has presented a dilemma for the Democrats, who oppose the killing of Soleimani but do not want to be seen as sympathetic to him because, as they admit, he was responsible for the deaths of hundreds of US troops in Iraq through the local militias he controlled.
Trump and House Republican leader Kevin McCarthy have accused Democratic House Speaker Nancy Pelosi of defending Soleimani.
She had called the killing of Soleimani "provocative and disproportionate" and "is not promoting peace, but an escalation" that puts Americans at risk, but she has also called him a "terrible person (who) did bad things."
The killing of Soleimani has isolated the US. Its NATO and other allies have not endorsed action and have criticised it.
Iraqi parliament approved a resolution demanding that the US withdraw its troops from the country. Trump has threatened sanctions if Baghdad went ahead with it.
The order to kill Soleimani was a turn around for Trump, who is under the shadow of impeachment, as he had opposed any direct action against Iran that some of his hawkish advisers like former National Security Adviser John Bolton had advocated.
According to some media reports, even Secretary of State Mike Pompeo had advised strong action against Iran, which is an obsession for many US politic.
Trump had called off at the last moment a missile attack on Iranian targets after Teheran shot down a US drone in June.
One of the collateral damages in the current standoff is a Ukrainian passenger plane that was shot down by Iranian forces that mistook it for a US aircraft last week killing 176 people on board.
(Arul Louis can be contacted at arul.l@.in)
( With inputs from IANS )