Luyendyk had been a top contender for the role after coming second in Emily Maynard's season of The Bachelorette earlier this year.
However, he has now taken to his Twitter page to deny rumors that he will be the next star of the ABC show.
"Just to clarify I will not be the next Bachelor," he said. "I am however pursuing opportunities in @Indycar & RolexSeries."
Luyendyk later tweeted: "The heart wants what the heart wants."
Elsewhere, E! Online reports that Olympic swimmer Ryan Lochte is no longer in the running after speculation that he could be the next star of the show.
The news suggests that Sean Lowe - who came third in Maynard's Bachelorette season - is a good bet for The Bachelor, although producers did hold castings earlier this year.
"We honestly briefly considered [Lochte]," a source said. "But we are going elsewhere."
The Bachelor's executive producer Mike Fleiss has previously promised fans that a decision will be made soon about the next star.
"We start shooting later this month," he tweeted on Monday. "A decision must be made this week. Who will be Bachelor 2013???"
On Wednesday, he added: "My hunch is that we will hear something tomorrow."
Maynard and her fiancé, Bachelorette winner Jef Holm, will appear on Good Morning America today (September 7).