Izzo was close to taking the Cleveland Cavaliers job in 2010, and has been at Michigan State for 19 seasons, compiling a 467-186 record, reaching six Final Fours and winning one national championship.
"There's been so many rumors over the years," Izzo said on ESPN. "I look at people I used to recruit against years ago [that] said that I'd be gone, but I'm still here and some of those schools have had three different coaches."
The Spartans play Virginia in the East Region semifinals on Friday.
"I've always said I'd never say never to anything because you never know what it brings. But I got so much more work to do here," Izzo said. "I have a great president, a great AD and a football coach that I really get along [with]. So this is a pretty good place for me right now. We're in a pretty good spot. Program's in pretty good shape.
"Ain't broke, so why fix it?"