Grimshaw, 28, is a decade older than the One Direction star, but the new Radio 1 Breakfast Show DJ told Heat that he does not notice the age difference.
"I don't feel protective - he's smart and savvy enough not to need a protector," he said. "He's probably wiser and more clued up about things than me.
"He's conquered America and all that, and I'm like, 'Let me tell you about the time I DJed in Milton Keynes'... He's like, 'I've just played Madison Square Garden, so I'm fine for advice, thanks'."
Grimshaw added: "He gets more attention than anyone I have ever, ever witnessed! It's so full-on.
"Having been on The X Factor as well, it's like people - quite rightly - think, 'I voted for you, so you pay me attention!'
"People wouldn't go up to, say, Rihanna the same way they go up to him."
Of their nights out, he added: "We do all sorts together. We're both Northern and we get on well because we've got a similar sense of humour."