The one stumbling block for a trade, according to Mike Giardi of CSN New England, is "some quibbling" over guaranteed money for Butler, a restricted free agent cornerback.
Otherwise, according to the report, the parameters for a deal between the teams are "mostly" in place.
Butler, 27, visited the Saints last week. He reportedly was irked by New England's signing of free agent cornerback Stephon Gilmore to a five-year deal worth $65 million.
The defending Super Bowl champion Patriots already pulled off a major trade with New Orleans earlier this month, acquiring wide receiver Brandin Cooks for a pair of 2017 draft picks -- a first- and third-round selection.
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.
Butler rose to fame following his Super Bowl-clinching interception of Seattle Seahawks quarterback Russell Wilson at the goal line to give New England a thrilling 28-24 win in Super Bowl XLIX.
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.