McBride, 27, played in just 15 games for the Saints the past two seasons with two sacks. He started eight games for the Lions in 2010, when he had a career-high five sacks.
McBride could be insurance for the Bears if they lose veteran free-agent defensive lineman Israel Idonije. Bears general manager Phil Emery has said the Bears are interested in bringing Idonije back but possibly at a reduced price.
Idonije signed a one-year, $2.5 million deal with the Bears last offseason.