The Saints have been linked to Butler for several weeks, and it was rumored that he would be part of a deal that sent wide receiver Brandin Cooks to the Pats, according to Dianna Russini of ESPN.com (via Pro Football Talk).
However, Payton noted Butler was never a part of the Cooks discussions, per Jeff Howe of the Boston Herald.
That deal trade didn't come to fruition, though, and New England instead acquired Cooks for the No. 32 overall pick in the 2017 NFL draft.
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The Patriots have a first-round tender on Butler, which means any team that signs him to an offer sheet will be forced to surrender a first-round selection.
Despite the uncertainty surrounding Butler's status, he visited with the Saints following the Cooks trade.
According to Nick Underhill of the New Orleans Advocate, Saints general manager Mickey Loomis said the following with regard to interest in Butler: "We're kicking the tires, I guess, is the best way to describe that. We'll see how that process works."
Butler's future with the Patriots first came into question when New England signed cornerback Stephon Gilmore to a huge contract in free agency.
Although the Saints have balked at surrendering a first-round pick to sign Butler, they could still acquire him via trade should they come to terms on a deal with the Pats.