Forecasters have predicted the weather system will hit Britain on Tuesday morning, bringing torrential rain and strong winds.
The Met Office has issued a severe weather warning covering most of Wales, north-west England and west Scotland.
Yellow “Be Aware” warnings of rain are also in place for Yorkshire and the Humber.
A spokesman said the system is the “remnants” of Storm Jonas, which has battered the US East Coast killing 18 people.
“There will be several low pressure systems which will work their way across the UK,” he added.
“We are in for some heavy rain and strong winds.
“The amounts of rainfall could be pretty high, there is potential for 50 to 100mm, which is four inches.
“Across northwest England and Scotland there could be upwards of 150mm, almost rivalling what we saw in December.
“These are quite wet areas and they are susceptible to flooding.”
The Met Office said the warning could be extended to south-west and south-east England.
The Environment Agency said it is monitoring river levels and has warned residents to “be prepared for the possibility of flooding”.
“We will monitor rainfall closely and urge communities to be vigilant,” a spokesman said.
“With heavy rainfall predicted in those areas there is obviously a risk of flooding.
“We will have crews out in the next couple of days and if the river levels rise then we could issue warnings.”
Storm Jonas brought hurricane-force winds and up to 60 cms of snowfall to the East Coast of America, bringing many states to a standstill.
Inbound and outbound flights from major airports across America were cancelled, at least 45 of which were coming from or going to the UK.
A state of emergency was declared across a vast swathe of the eastern seaboard, with schools and government offices closed, sports and entertainment events called off and thousands of homes without power.