The leaders are said to have discussed, among other things, a possible meeting between them in the United States.
The information comes amid escalating tensions between the countries after the United States carried out a series of deadly attacks off the coast of Venezuela this fall on what it claimed were drug-smuggling boats. Washington has blamed Maduro for part of the smuggling.
Several US warships are also in the waters of the Caribbean Sea near Venezuela.
Maduro has responded by putting the country on war alert.
At the same time, the two leaders have recently opened up for talks.
Although a meeting was reportedly discussed during the phone call reported by The New York Times, there are currently no concrete plans for such a thing, one of the newspaper's sources emphasizes.
