I find it kind of amusing.
The Spurs have a great player who doesn't want to play for them, and is one year from being a FA. No team likes to give away talent like that unless doing so improves the team. So, they're looking to get quite a bit of talent/draft picks in return for him.
The rest of the league realizes that 1) the Spurs have little to no leverage here, so they have little incentive to put together a blockbuster package, 2) that unless Kawhi signs an extension he'll be a 1-season rental, so without an extension agreed to as part of the trade, they have even less reason to offer a lot to the Spurs, 3) there are only a few teams that have the cap space, as well as players and future draft picks that could make a trade, so there isn't a bidding frenzy, and 4) Kawhi is a great talent at both ends of the court, but he quit on the Spurs this past season. Bottom line, Kawhi's trade value is not all that high, despite his considerable talent.
You put these two dynamics together, and it does not surprise me that new rumors appear every few days, and that no trade has been completed.
I could be misreading things, but my suspicion is that he will be traded, and that the Spurs will get a lot less for him than they have been seeking. If he were to sign an extension as part of a trade, that would increase what the Spurs would get in return, but Kawhi can likely make more on the market after next season AND get to pick which city he lives in, so there's not a lot of incentive for Kawhi/his agent to agree to that.