If the Clippers were able to keep only Paul, DJ, and Griffin, trade away all of their non-star players (Reddick, Pierce, Wilcox, and Dawson), renounce all of their free agents, and not sign their draft pick, they still wouldn't have enough to give KD a max contract with $69, 432, 666M in contracts and cap holds for 9 other players to fill out the roster.
Right now without trading any of their other pieces, which they legitimately can't since their supporting cast and bench is thin enough as it is, and renouncing all of their rights to free agents/draft picks this year, they have $78, 194, 482M in contracts, meaning they can only offer Durant a contract worth less than $16M this year, along with only Reddick, Pierce, and CJ Wilcox as their supporting cast.
It's not happening.
EDIT: Actually, their current ability is less than that, because I didn't factor in cap holds for roster spots. They're actually at $80, 929, 482M with the ability to only offer Durant around a $13M deal this offseason.