Preface: this is a silly rumor, it makes no sense, it's not happening under any circumstances. But it's out there and I feel compelled to at least comment on it.
Marc Spears from Yahoo! Sports floated the rumor a couple of days ago when he was a guest on John Canzano's Portland radio program. It involves the Los Angeles Clippers and Portland Trail Blazers swapping power forwards, with Griffin heading to Portland in exchange for LaMarcus Aldridge, who would have to be signed and traded.
Every team has to deal with these sorts of things. (One nice irony of this particular one is that Canzano's show is called "The Bald-Faced Truth" while this is a bald-faced lie.) Perhaps it's my imagination, but it seems like the Clippers have to deal with it more than other teams, perhaps due to the (no longer relevant) reputation of the club for incompetent management. I'm not even suggesting Spears didn't hear this from someone -- but he knows it's not true, and he started it by saying "This is a rumor" three times, but he said it anyway.
Blake Griffin turned the Clippers from a league laughing stock into a title contender. Not by himself of course, but he is the face of the turnaround. He is incredibly beloved by the fanbase. Aldridge is a great player, and he does some things better than Griffin, but no one can make a compelling case that he is actually a better player than Griffin. Meanwhile, what is undeniable is that Aldridge is three years older than Griffin. And that three years is KIND OF A BIG DEAL when you're talking about Aldridge, who would turn 30 before he ever played a game for the Clippers in this scenario. So you're talking about trading three years of Griffin in his prime for three years of Aldridge in decline, while paying more money for the privilege to do so since Aldridge will be looking for a maximum contract. In short, there is absolutely nothing to be gained for the Clippers in making such a deal, and plenty to be lost.
The stylistic differences between the two might be something to discuss, IF the Clippers were struggling in any way. News flash: they're not struggling.
It reminds me of the Carmelo Anthony rumors from awhile back. It's just sportswriters saying "Here are two names; let's say them in the same sentence and see what happens."
In this case, the process is pretty straightforward: Neil Olshey used to work for the Clippers, Aldridge is going to be a free agent, let's connect Aldridge to Griffin in a rumor that would have Griffin re-uniting with Olshey. Neither the Clippers nor Griffin would want any part of the deal of course, but ignore that.