Many rival teams had believed for months that Durant and Irving would team up next season — but that they would do so with the Knicks. In the halls of Oracle Arena, especially, fears that Durant was unfulfilled as a Warrior and talk of losing him to the Knicks were frequent topics among edgy Golden State Warriors team officials, coaches and, occasionally, players.

Across the country, Dinwiddie was “at the forefront” of the monthslong push to persuade Irving to prioritize the Nets over the Knicks and to nudge Durant in the same direction, according to one person familiar with the Nets’ pursuit of Irving who was not authorized to discuss it publicly.

The New York Times first reported last week that the Nets had also begun to heavily recruit the veteran center DeAndre Jordan, one of Durant’s closest friends, to form an incoming trio with Durant and Irving. Jordan spent the last two months of the 2018-19 season as a Knick, but two people briefed on the negotiations said Jordan also was convinced in recent days that Barclays Center would be a more hospitable backdrop for Durant and Irving than Madison Square Garden and joined the chorus promoting the Nets.

Some around the league believe Durant’s recent Achilles’ tendon tear, more than any James L. Dolan-related ineptitude, is what doomed the Knicks. Such thinking holds that if he wasn’t forced to sit out most or all of next season, Durant might have lobbied harder for Irving to follow him to the Garden. But one former N.B.A. All-Star, who requested anonymity because he was not authorized to discuss his colleagues’ plans, said Durant and Irving were already mentioning the Nets’ attractiveness as a free-agent alternative to the Knicks before the end of the regular season.