Star Trek: The Next Generation is one of the most beloved shows of the franchise, so it's wild in hindsight to think that anyone would've missed out on a chance to get in on the ground floor. Of course, hindsight is 20/20, and there were many back then who questioned if another incarnation of the original series was a great idea. As such, it's not too surprising to hear Spock actor Leonard Nimoy passed up on a chance at being an executive producer, though his reason why isn't what fans may think.
An excerpt from The Fifty-Year Mission: The Next 25 Years: From The Next Generation to J. J. Abrams: The Complete, Uncensored, and Unauthorized Oral History of Star Trek by Mark A. Altman is making rounds on the internet, and features Leonard Nimoy's explanation for not taking a behind-the-scenes position for the Patrick Stewart-led series. Nimoy had his reasons but explained it wasn't for the reason some might assume (via ScreenRant):
