Several Nigerien soldiers are also said to have died in the attack.
US Africa Command said the patrol had come under "hostile fire" and was working to confirm the details.
The US army has been providing training to Niger's army to help combat Islamist militants in the region, including the North African branch of al-Qaeda.
US President Donald Trump has been briefed by his chief-of-staff, John Kelly, about the attack, White House spokesperson Sarah Sanders said.
The paper said they were the first American casualties to die from hostile fire since the US Africa Command deployed in Niger.
Two wounded US soldiers are in stable condition and will be flown to Germany for treatment, CNN reports.
An official from Niger's Tillaberi region told Reuters that five Nigerien soldiers were among the dead.
Officials were unable to say who fired on the soldiers.
Militants belonging to al-Qaeda in the Islamic Maghreb (AQIM) - an affiliate of al-Qaeda - are active in the region and are known to have conducted cross-border raids.