Not this year.
Next year is when we maybe have a shot. Next year, they will have 3 key Free Agents, Kevin Durant (who will opt out), Andre Iguodala (expiring) and Steph Curry (expiring). They can resign Steph using his Bird Rights, but to be able to resign KD to a max, they'd have to renounce Iggy's rights, which puts the Warriors in a tough spot.
KD would eat all the cap room they would clear, and leaves them with the Room Exception (I think) to sign Iggy, which may not be enough.
This is where we should try and lure Klay. We can give them either Avery Bradley, Jae Crowder or Marcus Smart and multiple draft picks. It would clear enough room for GSW to resign all three. And with Durant on the fray in the Bay, we can convince Klay that he'll have a bigger role in Boston and he might push for the trade.
But chances are they let go of Iggy and just roll with their Big 4. But if we are trying to go for Klay, it should be next year. There's no chance they break up this 4 this year.
And this is assuming the cap will be at $102 million. If the cap is around the projected $107, then there's no need for the Warriors to clear room, they'll have enough to retain all three, which then will in turn, will not likely to trade Klay. I'm not even sure if I'm correct about this, please fact check me if I'm wrong.