The actor, who is currently starring in Attack the Block, told BBC News that he finds non-comic characters more rewarding to portray.
"I've always been funny as a kid, so it's not a challenge to me to be funny. It's the other stuff that's difficult, so I like to challenge myself," he explained.
Frost also revealed that his favourite role to date was as the protagonist in last year's TV adaptation of Money by Martin Amis.
"That's my favourite of everything I've done," the actor said. "We're trying to work on something similar, but I can't say any more."
He added: "I'm waiting for a Winston Churchill or a Henry VIII - I think you have to go with the physicality of your actor.
"I'm a bit too young for Churchill, but 20 more years and I'll be almost 60, and in ripe Churchill territory. And I could do the Bob Hoskins biopic in 20 years!"