The duo teamed up to write and record the original hit in 1984 and brought together the likes of Boy George, Bono, Sting, and Duran Duran to join them in the studio.
The track shot to the top of the charts and raised money and awareness about the plight of those starving in Africa.
Ure and Geldof revamped Band Aid in 1989 and again for the song's 20th and 30th anniversaries in 2004 and 2014, when One Direction, Ed Sheeran, Rita Ora and Sam Smith were among the performers, but the former Ultravox singer insists there won't be another cut of the single.
"I’m not sure music is the answer to it (human rights crises) now," he tells The Sun. "Thirty one years ago we did the Band Aid thing, it was the vehicle that people understood - you didn’t have video games, you didn’t have mobile phones and you didn’t have all of the distractions that you have today.
"Music was the be all and end all, so we used the medium at its peak. We used the power that music had at its peak.
"But maybe right now, the answer wouldn’t be a concert or a record - but I don’t know what the answer is."
Geldof might disagree with his old pal, but Ure says, "Bob’s getting quite old these days so maybe he's not the right guy."
"We text each other more than we see each other," he adds. "He texts me like a youth in text speech and emojis, and I can’t read it. So I spend ages trying to decipher what he’s sent, and then I answer him in proper dictation, proper English, with punctuation. But he answers in five seconds with more emojis and stuff, like a teenager... I can’t read what he says!"