The source told The Globe that Belichick initially told Moss, who's in the final year of his three-year contract, that he wouldn't be a part of the team's future plans.
But when Moss reported to camp in excellent shape, the source said Belichick reversed course and approached Moss about another contract. Moss apparently told Belichick it wasn't the right time to discuss a deal and that they should talk after the season.
Belichick indicated to reporters earlier this week that Brady didn't have a say in the deal, but The Globe reported that the quarterback "gave the deal his thumbs-up" before it was officially announced Wednesday.
In an interview that aired Sunday on "NFL GameDay Morning," Belichick reiterated to NFL Network's Michael Lombardi that the decision to trade Moss was strictly based on football.
"It was really just a combination of things," Belichick said. "Part of it was Randy, part of it was our football team, part of it was the opportunity to make the trade. Just in the end, when you put it all together, we felt it was the best thing to do for our football team."
Belichick also refuted the notion that he is giving up on a season in which he is fielding a young, developing Patriots defense.
"We're here to win, and that's what we're going to do," he said.