The Radio Free Asia (RFA) stated that the "experimental" new policy was confined only to the two provinces.
At one of the meetings, two Tibetan officials read from a government document declaring that "from now on, photos of the Dalai Lama can be displayed, and no one is permitted to criticize him by calling him names," a source told the RFA.
For decades, the longstanding Chinese policy was to force Tibetan monks and nuns to denounce the exiled spiritual leader. He has been described over the years as a dangerous separatist seeking to "split" Tibet away from China.
In Sichuan's Kardze prefecture, "an announcement has been made stating that photos of the Dalai Lama may be displayed, and that the Dalai Lama should not be criticized by name", a resident of the area told RFA's Tibetan Service on Wednesday.
Meanwhile, a Tibetan living in neighboring Qinghai province said, "there is no order from senior leaders to criticize the Dalai Lama."
Quoting a June 14 announcement by Tsepa Topden, a political studies instructor at Kumbum monastery's Qinghai Buddhist Institute, the source said, "Buddhist believers can have faith and show respect to the Dalai Lama. At the same time, he cannot be followed for political reasons," he quoted Topden as saying. "Religion and politics should be kept separate," Topden said, according to the source.
The 77-year-old Dalai Lama, who fled from Tibet into India after a failed 1959 national uprising against Chinese occupation, has been the face and symbol of the Tibetan struggle for more than five decades.
He handed over political power in 2011 to Harvard law scholar Lobsang Sangay, who was chosen head of the Tibetan government in exile in open elections, but the Dalai Lama remains the spiritual leader.