Charania says the Pistons will create a trade exception from the deal and acquire savings.
All three players are on expiring contracts, so they could be pieces to move at the trade deadline.
Prince averaged 9.2 points in 26 games with the Bucks last season while missing four months with a neck injury.
Harris averaged 2.7 points with the Bucks in his first season with Milwaukee, which signed him to a two-year deal.
LeVert averaged 7.4 points in 60 games for the Pistons.