Saints coach Sean Payton confirmed the planned meeting to the Associated Press on Tuesday.
The Patriots' restricted free agent cornerback was linked to the Saints in trade rumors surrounding wide receiver Brandin Cooks.
New Orleans traded their 23-year-old deep threat to New England last Friday along with a 2017 fourth-round draft pick for a first- and third-round pick this year.
Butler, 27, thought he would be a "Patriot for life" according to the Boston Herald, but was reportedly irked by the team's signing of free agent cornerback Stephon Gilmore.
Gilmore signed a five-year deal worth $65 million with New England.
As a restricted free agent, the Patriots have the right to match any offer for Butler. However, if New England releases his rights to sign with the Saints, the Patriots would receive New Orleans' No. 11 overall pick this year.
Last season, the former Pro Bowler had a career-high four interceptions as well as 48 tackles, 16 passes defensed, one sack, one forced fumble and two fumble recoveries.
The Saints also bolstered their defense on Tuesday with the reported signing of linebacker Alex Okafor.
Terms of Okafor's contract were not immediately reported.
Okafor, 26, spent his first four NFL seasons with the Arizona Cardinals, totaling 64 tackles, 13 1/2 sacks, four passes defensed, one forced fumble, two recoveries and an interception in 42 games.