The Kings, who started Beno Udrih at point guard for a majority of the 2010-11 season, appear determined to add a front-line floor general. Sources told ESPN.com's Chad Ford that the Kings have also contacted the Denver Nuggets about Raymond Felton.
A Parker trade would shift George Hill into the starting role, but sources also told Yahoo! that there are teams at the end of the first round interested in Hill.
Parker told French reporters last month that he thought the Spurs' chances at a title had ended. Parker later backed off those comments, saying the reporters got carried away with his remarks.
Parker was equally candid about San Antonio's diminishing title hopes in training camp last October. He said then that he felt the upcoming season was the last chance for the Spurs to win a fifth championship in the Duncan era, again pointing toward the team's aging core.
If this season was the Spurs' last chance, they mostly spent it playing that way. They carried the league's best record for practically the entire season and entered the playoffs with the No. 1 seed in the Western Conference. But the youthful Grizzlies beat the Spurs in six games, making San Antonio just the fourth No. 1 seed to fall in the first round.
Parker has spent his entire NBA career with the Spurs, arriving in San Antonio at the age of 19 and winning the starting job that season. He turned 29 last month and begins a four-year, $50 million extension next season.
He averaged 17.5 points and 6.6 assists last season.
Information from The Associated Press contributed to this report.