It has been assessing the likely results using world-leading forecast centres.
At the moment southern parts of the UK look as though they are most at risk during Sunday, followed by areas of North East Scotland on Monday. However, there is also the possibility that the depression could move across northern France as a weak feature.
The transition from a tropical to an extra-tropical feature is a particularly hard one to forecast with confidence, says the Met Office.
However, scientists believe the resulting depression will pass over, or close to, the UK from early on Sunday.
Chief Meteorologist, Paul Gundersen, said: “There is still some uncertainty surrounding this weekend’s weather, with the potential for heavy rainfall, strong coastal winds and large waves on Sunday. However, there is still a chance that the system may pass to the south of the country giving the UK a brighter day.
“Rain and strong winds may well bring disruption, especially across southern parts of the UK, with the potential for more than 50 mm of rain and coastal gusts of over 60 mph. People should stay up to date with the latest Met Office warnings.”
Craig Woolhouse, Environment Agency Flood Risk Manager, said: "Heavy downpours, some slow-moving, bring a risk of localised surface water flooding to parts of the Midlands, the north-west and eastern areas of England on Friday.
"On Sunday and Monday a combination of high spring tides and strong westerly winds brings a possible risk of flooding to the South West coast of England and along the Severn Estuary, while heavy rain may also lead to localised surface water flooding in parts of southern and central parts of England.
However, the forecast remains uncertain so we advise people to regularly check the flood risk situation over the next 48 hours.
"The Environment Agency is continuing to monitor the situation closely along with the Met Office and local authorities.
"People can sign up to receive free flood warnings, check their flood risk and keep up to date with the latest situation on the GOV.UK website to check if you are at risk of flooding or follow @EnvAgency and #floodaware on Twitter for the latest flood updates."