Amid reports that Jeff Van Gundy would not return as Rockets coach, Van Gundy said Sunday he has not decided to step down and Rockets owner Leslie Alexander said he has not reached any decision about Van Gundy's future.

Van Gundy has one non-guaranteed season remaining on his contract.

Told that there has been speculation that he would fire Van Gundy, Alexander said, "That's totally false.

"There is absolutely no truth to that. That's false, totally false. That decision has not been made."

Van Gundy strongly denied he had reached a decision. He has often said that the decision about next season was not only the team's, but said Sunday that he has not decided to step down.

"I haven't even thought about that yet," Van Gundy said. "It's just 12 hours after we lost. There has been speculation about my job going on the whole year. Anybody that saying that (that he has chosen to step down as Rockets coach), I have no idea why they would say that.

"There is no significance to anything other than we lost. That's the only significant thing."

Asked if he has meetings with Rockets general manager Carroll Dawson, assistant general manager Daryl Morey or Van Gundy planned to discuss Van Gundy's future, Alexander said that answering any "volatile questions" would lead to more speculation, but would only say he has not made a decision.

"Jeff has talked to you about that, and he wouldn't lie," Alexander said. "And I told you I haven't made a decision and you know I have never lied to you. Both stories are untrue. There is no truth to this."

But while Van Gundy remained the Rockets on Sunday, a day after the Rockets were eliminated in the playoffs' first round, neither could say how long that would remain true.