Sources confirmed Saturday that the Kings have inquired about Williams.
Yahoo! Sports reported that the teams have discussed a multiplayer swap that would send guard Darren Collison and forwards Derrick Williams and Jason Thompson to Brooklyn in exchange for Williams.
But sources close to the situation insisted that no deal is close. With Williams owed $63.1 million over the next three seasons, Sacramento must be sure about Williams to take on such a substantial amount of money, even though the Kings recently pursued Rajon Rondo and clearly are on the hunt for a point guard.
ESPN.com's Marc Stein and Ohm Youngmisuk first reported Dec. 9 that the Nets were shopping Williams and fellow former All-Stars Brook Lopez and Joe Johnson.
The Nets (10-15), owners of the NBA's highest payroll, have lost three straight games and currently sit in ninth place in the Eastern Conference.
They are 1-13 against teams .500 or better this season.
Williams, 30, is shooting just 37.1 percent from the field since Nov. 12. The Nets are 6-13 over that span.
Williams, who will make $19.8 million this season, is due $21 million next season and $22.3 million in 2016-17, although he can elect to opt out of his contract for that final year.
Williams is doubtful for Sunday's game against the Detroit Pistons due to a strained right calf, an injury he suffered Friday night in Cleveland.
He has had a litany of injuries during his time with the Nets, notably to his ankles.
Kings Interested In Deron Williams Deal
ESPNNewYork.com's Mike Mazzeo has the latest on the possible deal being discussed between the Kings and Nets for PG Deron Williams.