He told Australian magazine Woman's Day: "When people ask me about bands like One Direction, I say, I may not know them now, but if they are still here in five years, then ask me again."
Sir Cliff, however, conceded: "I must make the effort to YouTube One Direction.
"I'm sure they're good. You don't get famous like that without having something to offer."
Since appearing on The X Factor in 2010, when they finished 3rd, One Direction, which consists of Niall Horan, Zayn Malik, Liam Payne, Harry Styles, and Louis Tomlinson, have been unstoppable.
They have been credited with re-inventing the boy band market, won awards all round the world, are followed by adoring fans wherever they go, and are worth an estimated £30million.
The band is now attempting to conquer the movie world - a 3D film of One Direction will hit cinemas in August next year.
One website even named 2012 the year of One Direction.
Despite their phenomenal success, the boy band are, of course, no match for Sir Cliff, who has seen it and done it all.
In a career spanning more than 50 years, he has sold more than 250million records, is still one of Britain's most loved entertainers and is worth an estimated £60million.
He made his first movie - Serious Charge - back in 1959. And his calendar is still one of the best sellers.
No wonder he is taking his time to get round to One Direction. He admitted in the magazine interview that he had been impressed with some of the contestants on The X Factor on the occasions he had caught the show.
He said: "I've watched a couple of X Factor shows and I can't get over it. Even the losers are good! There are some fantastic singers around. I will make the effort to catch up."
Sir Cliff, despite his wholesome image, said it was time for modern-day stars to stop being so safe and rebel a little.
He also said they should bring the feel-good factor back to fans.
"I often feel the rock and roll world has lost its attitude of fun," Sir Cliff said. "It should be fun to create music; it should be fun to go on tour.
"The industry has become too strait-laced for me. It's not adventurous. It's too safe."
- Daily Mail