Speaking to the Daily Star, the indie rockers revealed that they had started discussions about hosting an event at Stamner Park.
The band said: "We have been talking about holding our own [festival] down south, somewhere like Stamner Park near Brighton where we live. We will do it in the next couple of years."
Explaining their plans, the band argued that festivals like Glastonbury had got too large and lost their "vibe".
"Although Glastonbury is the best in the world, something like that can't really carry on," said the group. "It's getting too big.
"We love playing Glastonbury, but we couldn't walk anywhere last year as it was so full. And [when] you have so many people there it's hard to get a vibe."
The rockers reached number one with their sophomore album Konk last week.
> Click here for our review of the album