Koepka, 31, has won four major titles with back-to-back victories at the US Open (2017, 2018) and US PGA Championship (2018, 2019) but still trails Woods on the major hunt by 11 and record holder Jack Nicklaus by 14.
"In my mind, I’m going to catch him [Woods] on majors," Koepka told the publication.
"I believe that. I don’t see any reason that can stop me.
"I’m 31. I have another 14 years left. If I win one a year, I got Jack.
"People misconstrue that as being cocky. No, that’s just my belief. If I don’t have that belief, I shouldn’t be out there.
"If you don’t think you can win, why the hell are you teeing it up? Yeah, I’m just going for second place this week. There’s a lot of that on tour. Even elite players are very happy with that.
"Second? Sports are made to have a winner and a loser. You’re one or the other."
Koepka may be winless in the majors for two years now but he did bounce back with his first win on the PGA Tour in 18 months following a one-stroke victory at the Phoenix Open in February.