"The ministry will examine the proposal and take a decision as soon as possible," the official told Reuters, requesting anonymity.
Saudi Aramco is a leading Saudi Arabian oil firm which produces, manufactures, markets and ships crude oil, natural gas and petroleum products to buyers around the world.
It supplies crude oil to Bangladesh regularly, the official said.
If a deal is finalised, Saudi Aramco will build the second oil refinery in Bangladesh. It will have an annual capacity to refine up to 8 million tonnes of crude.
Bangladesh's state-run Eastern Refinery Limited in Chittagong port city has a capacity to refine 1.4 million tonnes of crude a year.
Bangladesh will double its oil imports to nearly 6.5 million tones in the fiscal year ending June 2012 to run oil-fired power generating plants and meet increased demand by manufacturing firms.
Bangladesh's demand for fuel oil increases annually by more than 6 percent a year, officials said.