The 78-year-old farmer admits he has reached out to invite Robert Plant and his bandmates to the Glastonbury stage, but the rockers have repeatedly resisted his offers to reform.
However, he is not about to give up, and feels confident the group will get back together "one day".
In an interview with Ireland Am, Eavis says, "That will happen one day. I'm sure of it. They will do it."
Led Zeppelin's last official show was a tribute to their late record label boss Ahmet Ertegun at London's O2 Arena in December, 2007, when Plant and company were joined by Jason Bonham, the son of the late drummer John Bonham.
Eavis also told Ireland Am that there is one band he will never invite back to Glastonbury, but he refuses to name them.
Instead he reveals, "They aren't famous any more... they fell out."
This year's (14) Glastonbury festival, which takes place at Worthy Farm in Somerset, England from 25-29 June (14), will feature sets from Arcade Fire, Lana Del Rey, Lily Allen and Blondie.