The eye of the depression was 770 km to the east of Vietnam's Hoang Sa (Paracel) Islands Sunday afternoon with 50 kph winds.
In the next 24 hours, it is likely to move west-northwest at the 10 kph, and could grow stronger as it moves, according to the National Center for Hydro-Meteorological Forecasting.
As of Monday afternoon, it would be centered at around 450 km east-northeast of Hoang Sa with maximum wind speeds of 60 kph.
Due to the influence of the tropical depression in combination with a tropical convergence zone and a cold spell moving down from the north, almost all coastal areas of Vietnam would see heavy rains and rough seas, the center cautioned.
Storm Linfa had hit the central region of Vietnam, making landfall in Quang Nam and Quang Ngai provinces Sunday morning before reverting to a tropical depression.
The storm has uprooted dozens of trees, blown off the roofs of around 20 houses and sunk a fishing boat with a father and son on board in Quang Nam. Both of them are still missing.
Since the middle of this week, the entire central region and some Central Highlands provinces have been hit by torrential rains, causing serious flooding. In some areas, houses have been submerged almost four meters under water. At least eight people have died, seven are missing and 20,000 have been evacuated from their homes.
Linfa was the sixth storm to have formed so far this year in the East Sea, internationally known as the South China Sea.
The fifth one, storm Noul, killed six people last month.
Natural disasters, mostly floods and landslides triggered by storms, killed 132 people and injured 207 others in Vietnam last year.