The move comes less than one week after U.S. President Donald Trump announced plans to withdraw all U.S. forces from Syria.
"The U.S. Army has established two new military facilities in uninhabited parts of the province," Farhan al-Duleimi, a member of Anbar's provisional council, told Anadolu Agency.
The first base, he said, had been set up in the northern Rumana subdistrict (in Anbar's Al-Qaim district) near the Syrian border, roughly 360 kilometers west of provincial capital Ramadi.
The second base, he added, had been set up east of the city of Al-Rutbah, roughly 310 kilometers west of Ramadi and less than 100 kilometers from the Syrian border.
According to al-Duleimi, the twin bases are intended to help Iraqi forces "secure the country's borders and prevent infiltrations by the Daesh terrorist group."
"Scores of U.S. soldiers are currently stationed at the two bases, along with drones and other equipment," al-Duleimi said without elaborating.
The Iraqi government and the U.S. military have yet to comment on al-Duleimi's assertions.
But if confirmed, the construction of the two new bases will bring the total number of U.S. military bases in Anbar to four.
Roughly 5,000 U.S. troops have remained deployed in Iraq since the U.S. cobbled a coalition together in 2014 with the stated aim of fighting Daesh.
After its sudden emergence in mid-2014, the terrorist group managed to overrun roughly two-thirds of Iraq, mainly in the country's north and west.
Along with training Iraqi forces, the U.S.-led coalition continues to provide the Iraqi army with air support as it hunts down and destroys the terrorist group's lingering presence.
Last December, Baghdad declared that Daesh's military presence in Iraq had been all but destroyed following a three-year conflict that ended with the fall of Daesh-held Mosul.
Iraqi officials, however, continue to wage frequent operations against Daesh "sleeper cells," which allegedly remain active in certain parts of the country.