The 65-year-old actor insisted he doesn't "think about it that much" but admitted things could be different when he gets older.
He told The Observer magazine: "At this point, mortality doesn't scare me. Check back in with me when I'm on my deathbed... but I don't think about it that much. Only every once in a while."
However, one recent incident made him consider the "mortality thing", when his and wife Kyra Sedgwick's dog died last year.
He said: "We looked at each other. And I went, 'Let's do the maths here. I don't think I'm ready for another 15 years of picking up s***.' That's the only time I've thought about the mortality thing. Related to an animal."
Kevin and Kyra, 58, have been married since 1988 and he believes communication is key to their long-lasting union.
He said: "We're pretty good at leaving our work at the office. The thing about it is, Kyra's the type of person who would be very clear if her emotional needs weren't being met in some sort of way. If the core piece of our love and our marriage was getting short shrift, she would bring it up in a heartbeat. And we would work through it."
The pair have children Sosie, 32, and Travis, 35, together and Kevin admitted he and Kyra will never stop worrying about their kids.
He said: "I'm always thinking about 'em. We kinda had this idea, both Kyra and I, that when they got to 18 we'd say to ourselves: 'All good!' That's not really what happens."