On Wednesday, the New York Daily News, citing unidentified "close friends," reported Parker might welcome a trade to the Knicks.
Parker, who is married to "Desperate Housewives" star Eva Longoria Parker, on Wednesday called that story "even worse than the paparazzi," according to the San Antonio Express-News.
On Monday, Parker told reporters he wants to stay in San Antonio, adding that he trusts coach Gregg Popovich and general manager R. C. Buford to make the right decisions for the Spurs' roster.
"Again, I want to make it clear: I want to stay in San Antonio," Parker said Wednesday, according to the Express-News. "My heart is in San Antonio. But it doesn't seem to matter what I say. The rumors get worse and worse, and as I go through my free-agent year, I know there will be even more."
Parker's contract expires after next season. The three-time All-Star is expected to seek a maximum contract extension.
The Daily News cited Parker as a backup plan for the Knicks, should their attempts to sign LeBron James or another high-profile free agent falter. The story cited "close friends" of Parker saying he and his wife would "love to relocate to New York."
Parker shot down that part of the report, saying it came from "a source who told a source who told a friend who told somebody else," according to the Express-News.
Parker remains optimistic that he and the Spurs will reach an agreement on a contract extension this fall, according to the report.
"I'm happy in San Antonio," Parker said, according to the report. "My wife and I are very happy. I built my home base here, so why wouldn't I want to be here?"
On Thursday, Parker said he won't play at the world championship for France this summer and will instead stay with the Spurs.
The 27-year-old point guard said on his website that the Spurs made it clear he should "only focus on the club."
Parker says his decision is "irrevocable," adding that his NBA season had been hampered by injuries and that the Spurs don't want to see him so beaten up again.
The world championship is Aug. 28-Sept. 12 in Turkey.
Information from The Associated Press was used in this report.