Though weakened into a tropical storm, it continued to bring heavy rain and blustery winds to the Southeast as it pushed inland, soaking areas still recovering from last month's Hurricane Florence.
In October 2017, strong winds from Hurricane Ophelia, which travelled north off the coast of Portugal and western Spain, fed forest fires that killed around 40 people during a heatwave.
Leslie was set to make landfall in the Lisbon area overnight on Saturday, by which time it is expected to have been downgraded to a tropical storm.
As of Saturday afternoon, Leslie was about 200 miles (320 km) west of Lisbon, the NHC said, adding that it is expected to become a post-tropical cyclone and dissipate by Sunday night or Monday.
Leslie first became a sub-tropical storm almost three weeks ago on September 23.
Portuguese authorities had urged those living by the coast to batten down and stay indoors amid warnings of high winds which reached 176 kilometres per hour (110 miles per hour).More news: Woman who bought shredded Banksy Girl With Balloon painting to keep it
Leslie caused a lot of tree damage in the Portuguese seaside town of Figueira da Foz.
More than 15,000 homes were reported to be without power, while several flights to and from Lisbon were cancelled.
The storm, one of the most powerful to ever hit the country, is now passing over northern Spain.
The A1, the main motorway running through Portugal, was temporarily blocked by a fallen tree, authorities said.
More than 300,000 homes lost electricity as the storm passed, said Belo Costa, commander at the Civil Protection Agency.
Separate storm fronts in the north and east of Spain mean heavy rain is expected across much of the country on Sunday.