The rockers have yet to perform at the massive music festival, which takes place in Somerset, England and Ulrich is adamant their chances of organiser Michael Eavis choosing them are fading.
He tells MTV, "Every year there's probably less chance of us doing it than the previous year, but it just looks like it would be a fun night out.
"We've been fortunate enough to play every other festival on this planet numerous times, so Glastonbury is the only one that's eluding us.
"There's such a vibe and it's maybe the most quintessentially English festival. Everybody who goes there loves it and obviously Michael doesn't need our help - I completely appreciate and respect that - but if he ever wants to get hold of us we're in the Yellow Pages and ready to go!"
Eavis has already revealed that next year's (14) three major headliners have not previously played at the event.
He said, "They're three bands who haven't played Glastonbury, and that's important. There aren't many bands left who haven't played the festival, and before we run out I'd like to persuade the ones on my wish list to come down. I think I've managed that with these three."
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