As C's fans we have Trader Danny, any player could be traded at any time if he thinks it makes the team better in the long term, even if the team has to take a step (or two or three) back in the short term.
I don't think GM Doc Rivers is the same type of guy, similar to his coaching style. He's a players coach that the veterans love to play for. Remember how he used to say "nobody has ever beat our starting 5 (when it consisted of Rondo/Ray/Pierce/KG/Perk) in a 7 game series"? I'm sure he feels something similar about his current Clippers team.
Sure if we had a big name vet in decline, then sure I could see Doc making a Billy King type move and trading Blake Griffin straight up for Dwyane Wade or something like that, but beyond that I really struggle to see Doc as the GM willing to break up that core. He doesn't know how to rebuild or retool like Danny does, he just knows how to tread water with what he has. Sure, he's had talks with other teams, but unless it's an equal level star (or big name star) coming back in return (like Blake for Paul George), I don't see a trade happening. Definitely not one that involves the C's in a 3 way where they end up getting Blake.
Really, I don't see GM Doc trading Blake or CP3 any time soon.