The Saints added tight end Benjamin Watson in the offseason.
Fleener, 29, signed with the Saints in free agency in 2016 after spending his first four years in the league with the Indianapolis Colts.
Anderson played for five years for the Broncos before being released in April.
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The Saints are on the for hook now for $8.2 million in dead cap money. Last week, they inked deals with Ohio State quarterback J.T. Barrett, South Carolina guard Cory Helms, Cincinnati defensive back Linden Stephens, Minnesota tight end Nate Wozniak, Mississippi State defensive back J.T. Gray and Tennessee linebacker Colton Jumper.
The Saints also didn't get what they were hoping for in Fleener, who totaled just 926 yards and five touchdowns across the last two seasons.
Fleener saw his role in the Saints offense significantly reduced last season as he had just 22 catches (on 30 targets) for 295 yards, his lowest numbers in his rookie season. The amount absorbed this year will drop to $5 million has been designated a post-June 1 cut, meaning that $3.2 will be on the 2019 cap. He had a career year in 2014 when he had 774 yards on 51 catches and eight touchdowns.