He said the President planned to look at "all" aspects of how the US deals with its historic enemy, which lies just 90 miles south of Florida.
Human rights would be a key part of Mr Trump's revised policy towards Cuba, the press secretary said.
During the final years of the Obama administration, the US softened its stance towards its communist neighbour.
Mr Spicer's comments suggest Washington may take a harder line with Cuba, raising the possibility of new trade embargoes and the cancellation of commercial flights from the US, which were only recently introduced.
Under Barack Obama, the US ended a policy that allowed any Cuban who made it to American soil to stay and become a legal resident.
Ending the so-called ‘wet foot, dry foot’ rule was welcomed by Havana as “an important step in advancing relations”.
Mr Obama and Cuban President Raul Castro established full diplomatic ties and opened embassies in their capitals in 2015. The former US President visited Havana last March.
But Mr Trump has threatened to end the period of improving relations.
In November he tweeted: “If Cuba is unwilling to make a better deal for the Cuban people, the Cuban/American people and the U.S. as a whole, I will terminate deal.”
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