The soldiers, part of the US Naval Forces Central Command (NAVCENT) which is headquartered in Bahrain, had been asked to leave the coalition and may depart within the next 48 hours, the source told AFP.
"The Bahrainis told the US general in command of the base that Qatari soldiers must leave," the source said on condition of anonymity.
"They are still in the base but likely to leave within the next two days."
Qatar denies the charges.
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Direct tensions between Manama and Doha have been further exacerbated after Bahrain accused Qatar of directly interfering in its internal affairs.
Qatar has also denied those charges.
The source did not detail the number of Qatari troops based in Bahrain. One analyst estimated it was no more than a "handful of officers".
Qatar has deployed troops with NAVCENT since 2014, according to one official.
As part of their operations, numerous air strikes against IS targets in Iraq, Syria and Afghanistan have been conducted from Qatar's Al-Udeid, the largest US base in the region.
Washington is involved in diplomatic efforts to resolve the impasse in the region but US policy has proved unpredictable.
President Donald Trump has sided with Saudi Arabia and its allies, including Bahrain, the UAE and Egypt, claiming Doha had "historically been a funder of terrorism at a very high level".
However, Pentagon and State Department officials have scrambled to reassure the emirate.
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