The state-owned company was seeking between 1.1 million tonnes and 1.28 million tonnes of 500ppm sulphur gasoil, 100,000 tonnes of jet fuel and 120,000 to 140,000 tonnes of 180-cst high-sulphur fuel oil.
Unipec, the trading arm of China's state-owned Sinopec , placed the lowest offer for the gasoil and jet fuel cargoes, beating eight other traders, two BPC officials familiar with the matter said.
It has offered to sell gasoil to Bangladesh at a premium of between $3.05 and $3.08 per barrel to Middle East quotes and offered jet fuel at a premium of $4.10 a barrel, they said.
Emirates National Oil Co (ENOC) made the lowest offer for fuel oil cargoes, against five other companies.
The trader a $17.80 a tonne premium to Singapore spot quotes for high-sulphur furnace oil.
"Unipec is likely to win the tender for both gasoil and jet fuel, and ENOC will get the tender for fuel oil as they came up with the best prices," one of the officials said.
"The deal will be finalised by the end of this month after verifying all other details," the official added.
The tender closed on April 11 and was expected to be valid for 75 days to June 24.
BPC resumed issuing tenders for long-term contracts in February, 2016 after a 15-year hiatus, during which it negotiated directly with suppliers of fuel products.
It wants to move away from direct deals as part of efforts to buy at cheaper rates.
A shortfall in supplies of natural gas has forced the South Asian country to burn oil, a costlier option, to generate electricity.
Bangladesh typically imports about 3.2 million tonnes of diesel and 2.5 million tonnes of fuel oil annually, making it one of the top 10 such importers in the region.
Currently, BPC has term contracts with 10 companies for refined oil product imports.
BPC also buys 700,000 tonnes of Murban crude from Abu Dhabi National Oil Co annually and another 600,000 tonnes of Arab Light from Saudi Aramco for its only refinery.
Bangladesh, with more than 160 million people, also plans to tap currently cheap and plentiful global liquefied natural gas (LNG) supplies to fill a domestic supply shortfall.
Reporting by Ruma Paul