Met Eireann have issued two Status Yellow weather warnings as up to 35mm of rain is set to lash the south and east.
A rainfall alert is in place for Cork and Kerry since 3am on Monday morning and will remain in place until 4pm this afternoon.
And another rainfall warning will also be in place for Dublin, Carlow, Kildare, Kilkenny, Wexford, Wicklow, Tipperary and Waterford between 9am and 8pm on Monday.
The national forecaster said: "25mm to 35 mm rainfall on Monday, with a risk of spot flooding".
And meteorologists have warned we could see some severe weather as the tail end of Hurricane Lorenzo is expected to reach Ireland later this week.
Met Eireann said: "This morning will start dry in most places with patchy fog clearing to give some brighter spells.
"However, rain along the southwest coast will spread up over the country during the day, with some heavy falls likely, and reaching the north of Ulster in the evening.
"Somewhat drier conditions will develop in the southwest in the afternoon.
"Maximum temperatures 13C to 16C and becoming breezy and blustery with the rain."
Heading into Tuesday, it will start out rather damp, blustery and cloudy with patchy rain and drizzle.
Later in the day, bright and clear conditions weather will gradually extend from the west and northwest during the morning but the southeast may remain cloudier.
It will be rather cool during the day with highs of just 12C to 15C and Tuesday night will be noticeably chilly.
A forecaster said: "Minimum temperatures dropping to between 2C and 6C under clear spells, with a risk of grass frost."
Wednesday looks set to be a dry and pleasant day with highs of 14C but the tail end of Hurricane Lorenzo is heading towards our shores and is expected to make landfall by Thursday.
The hurricane, which is likely to become a tropical storm by the time it reaches Ireland, has reportedly made history by becoming the strongest hurricane on record this far north and east in the Atlantic basin, according to the National Hurricane Center.
A Met Eireann forecaster said: "On Thursday Lorenzo is likely to be in the vicinity.
"Its exact track and central pressure is very uncertain as is the timing. It is possible it could track to the West of Ireland.
"It will become milder due to the influence of the tropical origin air. The risk of severe weather continues and the progress of Lorenzo and any potential impacts for Ireland are being closely monitored by Met Eireann."
