Sources confirmed Saturday that the Kings have inquired about 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.
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 was ruled out 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.