An American official told the broadcaster ABC that a US navy ship had been in the area to monitor the situation and to provide assistance.
The US says the al-Shabab group, which is fighting against the Somali government, has links to al-Qaeda.
Bryan Whitman, a Pentagon spokesman, had said earlier on Monday that he would not comment on the operation or on any potential US involvement.
But Al Jazeera's senior Africa correspondent Andrew Simmons, reporting from the Kenyan capital of Nairobi, said US sources say they are confident they have their target.
"[If confirmed] it will certainly be a major tactical victory on the part of the US special forces," Simmons said on Tuesday.
"But politically, apart from a blow to al-Shabab, this will not have any major significance."
Nabhan is believed to have owned the lorry used for the 2002 bombing of an Israeli-owned hotel on Kenya's coast that killed 15 people. He was also wanted over a failed attack on an Israeli airplane leaving Mombasa airport the same year.
He is thought to have fled to Somalia afterwards.
Several residents in Barawe said Nabhan had been killed in the Barawe attack, along with at least one other person.
Abdi Ahmed, a resident, said six helicopters flew over the village before two of them opened fire. "White" foreign soldiers in military uniforms then got out and left with two wounded men, he said.
Al-Shabab confirmed to Al Jazeera that the attack had taken place, but refused to give more details.
Earlier reports suggested that the helicopters were French, but the French military denied its troops had been involved.
Barawe district, about 250km south of the capital, Mogadishu, is controlled by al-Shabab fighters.
Commenting on the Somalian conflict, Ernst Jan Hogendoorn, Horn of Africa project director at the International Crisis Group, said that the solution to Somalia's problems will have to be a political one.
"We feel … that there are many moderate elements in al-Shabab that could be brought into the government, he told Al Jazeera from Nairobi.
"It is unclear how deep the connections between al-Qaeda and al-Shabab are. Although this may be an important strike against a particular individual, in the long run this is not the way the war on terror is going to be won in Somalia."
Noting that the US had been looking for Nabhan for some time, Abdi Ismail Samatar, a professor at the University of Minnesota, said: "Obama's policy in Somalia has been more aggressive despite the fact that the president, in his address to the Muslim world in Cairo, said that the US does not intend to intervene in the local political affairs of other countries.
"But the government, since January this year has been deeply interventionist.
"[It] has been deeply involved in Somalia and has been in fact more aggressive than the Bush administration to the point where they sent two arms shipments to the Transitional Federal Government, which the Bush administration never did."