The 31-year-old Beck had a stint with the Texans in 2012 but did not appear in a regular-season game. Houston released him in October.
In addition to starter Drew Brees, the Saints have veteran reserve passers Seneca Wallace and Luke McCown and undrafted rookie Ryan Griffin under contract. Griffin, a Tulane product, will also take part in the minicamp that runs Friday through Sunday.
Rookie wide receiver Duron Carter, who tried out for the Vikings last weekend, is also slated to try out for the Saints. Duron Carter is the son of Hall of Fame wide receiver Cris Carter.
Seventy players are slated to take part in the weekend workouts, the Saints said. There will be two practices on Friday and Saturday and one on Sunday.
Other veterans trying out for the Saints this weekend include defensive lineman Brian Schaefering, who played for now-Saints defensive coordinator Rob Ryan in Cleveland and Dallas; and offensive lineman Quinn Ojinnaka, who made five starts at left guard for St. Louis last season.