"Send him to Gitmo, I would certainly consider that," Trump told reporters at the beginning of a cabinet meeting, using the nickname for the jail site.
Authorities say Saipov, an Uzbek immigrant who moved to America in 2010 and is not a US citizen, used a rented pickup truck to mow down pedestrians and cyclists along a mile-long stretch of a bike path on Lower's Manhattan's West Side on Tuesday.
Eight people were killed in what has been termed a terror attack carried out by Saipov, who left a note saying he carried out the attack in the name of terror group ISIS.
Guantanamo gained global notoriety when Islamist fighters who were captured in Afghanistan were put there in the months following the US-led invasion.
The prison only houses non-US citizens, with American accused jihadists processed in federal court.
The population has shrunk from a high of more than 750 down to 41 after years of attempts by Barack Obama's administration to shutter it amid claims of abuse and a lack of due process.
In the face of Republican opposition, Obama never succeeded and Trump has taken a different track, saying as a candidate that he wants to load up Guantanamo with "some bad dudes."