Monroe wants rookie Max, which is kinda a lot. And Matthews is a complete unknown until September. Who is willing to gamble? Kings certainly don't have free money
List of players, that will be reasonably available to Kings consists of guys, that are either a)minor priority for their team to resign, b) their team might not be able to afford, or c) their team just doesn't want to retain.
It's obviously not that long, but among bigs and guards/wings, that are any good my list will come down to
a) Belinelli (replaces, what Stauskas can become in the next 2-3 years, so probably might just well trade Nik, if he has any reasonable value for someone)
b) Stuckey (Pacers can only pay him MLE and offer backup role, so $1 million more and a chance to compete for starting spot might interest him; same about Nik), Kyle O'Quinn (pretty big gamble for MLE+ money, that will be needed for Magic not to match, but KOQ will likely shop for the best contract, he can find, so will be available later in the process, and should be a target, if better players go elsewhere)
c) Amir Johnson (Masai didn't mentioned him at all in his season-ending PC, and Amir's comments had "please take me back" - he likes it very much in Toronto - feeling to them), Chandler (if there's some truth to DJ rumors and Dallas will entertain this thought, Chandler might look elsewhere, though both LA teams and NY become heavy competition)
I know, that Grizzlies play Koufos as a PF next to Gasol in Portland series, but that's because they can get away with it. Koufos is 90% center, which won't work, if Boogie and JT are the other two in big man rotation. Chandler OTOH might.