A National Investigation Agency (NIA) team is likely to join the investigation shortly, Inspector General of Police, Patna zone, N H Khan said.
The two bombs were found from the pilgrimage centre after an explosion-like sound was heard amid stringent security measures in view of the Dalai Lama's stay.
"We have thoroughly sanitised the area where high security measures have already been there in view of the importance of the place. CCTV footages are being collected for investigation.
The bombs were found in the vicinity of the Kalachakra ground during an intensive combing operation by a police team led by DIG (Patna Range) Vinay Kumar, Khan had earlier said.
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The explosion-like sound was heard shortly after the Dalai Lama completed his discourse and retired for the day at a Tibetan monastery, he said.
"During the operation, a burst thermos flask was found at the kitchen. This might have caused the sound," the IGP said.
"The two suspected explosive devices have been taken to a secluded spot where they could be defused safely. A bomb disposal squad has been rushed to Bodh Gaya. It is not yet known what material these suspected explosive devices are made of but experts available locally have said they were unlikely to detonate on their own," Khan said.
The Tibetan spiritual leader had arrived in Bodh Gaya on January 1 and he is likely to stay there for a month.
In 2013, the Maha Bodhi temple, situated at the spot where Buddha is said to have attained enlightenment, was rocked by a series of explosions in which five people, including two monks, were injured.