Bangladesh grades storms with signals ranging from 1 to 10, and authorities start major preparations when the signal is raised to five or beyond.
"Bijli is gaining strength as it continues to move towards the shorelines and may hit the coast by Friday night or Saturday morning," a meteorology official told Reuters.
Officials at Cox's Bazar said there were plans to close flight operations at the Chittagong airport from Friday evening, while cyclone shelters have been prepared to accommodate up to a million people along the coasts.
Low-lying areas in several coastal districts and on offshore islands may be inundated by tidal surges up to three metres above the normal tide.
Officials said security, rescue and medical workers including Red Crescent volunteers were on alert for a possible evacuation of millions of people from low-lying areas.
"This may not be a big cyclone, but we are getting prepared anyway," Mukhlesur Rahman, a senior official at the food and disaster management ministry, said.
Cyclones and tropical storms are common in Bangladesh, killing many people in the delta nation of 150 million every year, and causing huge damage to crops and property.
A devastating cyclone in April 1991 killed about 140,000 people, while Cyclone Sidr swept part of the coast in November 2007 killing at least 3,500.