Garoppolo's name has been bandied about in trade rumors for months now, and Butler, a restricted free agent, has yet to sign the first-round tender the Patriots placed on him last month. Instead, the Saints are believed to covet Butler in exchange for the No. 32 overall pick they received in the trade that sent Brandin Cooks to New England.
Amendola was set to make $6 million in salary in 2017, and it was relatively clear he was not going to be playing for the Patriots under his contract the way it was structured. If that doesn't happen, the Saints are expected to offer the Patriots a trade for Butler once he signs his $3.91 million tender. Butler wants a long-term contract, and as the Patriots aren't interested in paying him what he thinks he's worth, there have been discussions of a possible trade to a team that would sign Butler to the kind of deal he wants.
"We had a chance to visit with him", Payton said of Butler at the time.
The deadline for restricted free agents to sign offer sheets is Friday.
"In fact, I know we're not going to do that".
Butler has played in 43 regular-season games with 33 starts, including starts in all 16 games over the last two seasons for the Patriots.
The Atlanta Falcons are on New England's home schedule this season and could have been an option for a Super Bowl rematch in Week One.
He had the game-clinching interception that allowed the Patriots to win the 2015 Super Bowl against Seattle.