According to the report, coast guards in the country have been informed and the hunt is on to locate them despite adverse weather conditions.
The missing Indians are all said to be from Tamil Nadu.
"They went for fishing as usual but have not returned yet. What I suspect is that they been hijacked by pirates," Saeed Rashid, owner of the fishing boat, told Times of Oman newspaper.
The boat reportedly went missing from al-Ashakara coast on Thursday evening.
"They went to fishing to the inner sea. What we learnt is that they ran out of fuel and were stranded in the sea. They might have been kidnapped from there," Rashid said.
The report also quoted International Maritime Bureau's anti-crime arm as saying that on Wednesday, an LNF tank was attacked by pirates off the coast of Oman.
There are increased concerns over the pirates extending geographic range of their operations.