Bogdanovic told The Sacramento Bee on Tuesday that he has received a four-year, $51.4 million offer but has not decided whether he will sign it.
"They did, but we will wait to see," Bogdanovic told the newspaper of the offer. "Maybe we will sign tomorrow. Maybe we sign in a month. Who knows? We will see."
Bogdanovic, who averaged 14.1 points, 3.8 assists and 3.5 rebounds per game for the Kings last season, will play 2019-20 on the final season of a three-year, $27 million contract.
The 27-year-old told the Bee that he wants to stay in Sacramento but would not rush into signing a deal.
Bogdanovic would be a restricted free agent in the 2020 offseason.