Citing unnamed sources, ESPN said James is among a number of top players who are interested in competing in Paris while The Athletic said the Los Angeles Lakers forward has already called multiple stars in a bid to recruit them.
James has not played for Team USA since he won a gold medal at the 2012 London Olympics.
James, a three-time Olympian and two-time gold medallist, reached out to Kevin Durant, among others, and the two players are viewing the Paris Games as a "last dance" with USA Basketball, sources told The Athletic.
Curry has never represented the United States at an Olympics but ESPN said the NBA's all-time leader in three-pointers has expressed an interest in playing for Steve Kerr, his Golden State Warriors coach.
James' push to recruit players started well before the United States lost in the bronze medal game of the recently-concluded FIBA Basketball World Cup and his decision was not related to that team's result.