Northern Ireland is expected to experience “slow moving thundery downpours” and the tail-end of Storm Alex as the week progresses.
The tropical rainstorm has caused flooding in south Florida and was responsible for a number of deaths in Cuba.
However, by the time it reaches UK shores Storm Alex will have lost much of its strength.
The Met Office has said that after a mostly dry and fine start to the week, some wet and windy weather is on the way.
A low-pressure system that was responsible for some of the unsettled weather over the weekend is now out in the North Sea, leaving behind some showers for eastern coastal areas on Tuesday.
From late on Tuesday, a more concerted change is on the way, with the arrival of a low-pressure system in the west that will first bring showers to the southwest and Northern Ireland late on Tuesday and into Wednesday morning.
This low-pressure will continue slowly tracking east across the UK on Wednesday and brings with it the risk of some slow-moving thundery downpours across northern areas of the UK, although precise positioning is still being determined.
Met Office Deputy Chief Meteorologist Adam Thornhill said: “The low-pressure on Wednesday will bring showers to most areas of the UK, but the heaviest, slow-moving downpours are expected in northern areas, including Northern Ireland, with a chance of associated thunder and lightning.
"Although rainfall amounts are still open to some uncertainty, there’s a chance some areas in the north could see in excess of 20mm of rain within a three-hour period.
“This will largely break up later in the day on Wednesday, leaving behind just a few showers by the late evening.”
The unsettled theme is to continue later in the week when the remnants of ex-tropical Storm Alex, which brought heavy rain to southern Florida in recent days, tracks to the northwest of the UK from the Atlantic and will bring with it some high winds and rain, albeit to a much lesser extent than was seen in America.
Mr Thornhill continued: “By the time ex-tropical Storm Alex gets near UK shores, it will have transitioned into a mature Atlantic low.
"Although it will have lost much of its strength, it will bring some unseasonably strong winds across the UK – especially to the northwest on Thursday and Friday.
“The track of the former storm currently looks to be grazing the far northwest of the UK on Thursday and Friday and, although the details are still being worked out, winds could be around 45mph for most in the north of the UK, with a chance of some gusts in excess of 55mph in some exposed northwestern island and coastal areas.”
Although much will depend on the positioning of ex-tropical Storm Alex late on Friday, the weather through the weekend looks likely to be a mix of sunshine and showers – which could be heaviest in the northwest – with some breezy conditions likely to persist in the far north.