According to Mike Giardi of CSNNE, Butler was in favor of being shipped from the defending Super Bowl champions to the Saints.
"He wanted New Orleans. He wanted them badly," Giardi wrote. "They couldn't work out a deal. So what's he supposed to do now? Sit at home? No, you suck it up.
"You have to turn yourself back into a Patriot at least for a year and hope. Who knows, maybe you do your work and maybe they say, 'Hey, Malcolm, you know what, we can't give you [Stephon] Gilmore money. But maybe we can find something. Maybe we've got $10 [million] or $11 million."
Butler reported to the Patriots' voluntary workout Wednesday despite not having a long-term contract in place.
In April, he signed a one-year tender that will pay him $3.91 million in 2017.
The Patriots and Saints flirted on the trade front, and while that did result in New Orleans sending wide receiver Brandin Cooks to New England, Butler wasn't part of the deal.
Butler visited with the Saints in March and held contract talks, but in order to orchestrate a trade with the Pats, New Orleans would have had to sign him to an offer sheet and surrender the No. 11 overall pick in the 2017 NFL draft.
Neither of those things happened.
While New England has been unwilling to sign Butler to a long-term deal thus far, it did ink Gilmore to a five-year, $65 million contract in free agency, per Spotrac.
The 27-year-old Butler is a one-time Pro Bowler and is coming off his best season, with four interceptions in 2016.