Punjab suffered their eighth loss in 12 games and bowed out of the competition
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 said.
"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."
The news comes as the Gulf faces the biggest diplomatic crisis in recent years, with Saudi Arabia, UAE, Egypt and Bahrain suspending ties over Qatar's funding of extremists.
The source did not detail the number of Qatari troops based in Bahrain. One analyst estimated it was a 'handful of officers'.
Qatar has deployed troops with Navcent since 2014, according to one official.
Navcent is part of the US Central Command whose area of operation includes the Middle East and Asia.
As part of their operations, numerous air strikes against Daesh 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. President Donald Trump has backed Arab states, claiming Doha had "historically been a funder of terrorism at a very high level".
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