It comes after suggestions that the young boy band are provoking a Beatlemania-style reaction in the US and Canada.
The What Makes You Beautiful hitmakers have been mobbed during public appearances on the other side of the Atlantic and last week became the first British group to debut at number one in the US.
Sir Paul said: "There are so many bands who all get called 'the next Beatles'. Suddenly it puts an awful lot of pressure on them to be the next Beatles."
Speaking to ITV1's Daybreak, he continued: "Oasis were 'the next Beatles' once, if you remember. It's a pressure, because suddenly you've got to live up to all the things that we did, and it was a different time.
"So let's just call them 'the next terrific band'."
Sir Paul, 69, did wish them well with their career in the States.
"They're doing well in America. It's good. Good luck, lads," he added.
ONE DIRECTION'S FAMILY ALBUM