Khloe Kardashian, Lamar Odom Not Ready for Divorce ... The Door's Open a Crack

Khloe Kardashian and Lamar Odom are NOT ready to divorce ... in fact, they're secretly talking.

Sources connected to both Khloe and Lamar tell TMZ, the 2 of them are not romantic and are not talking reconciliation, but they don't want to close the door on the marriage either. That explains why Khloe's divorce has been laying dormant in the courts for more than a year ... the judge has even said if she doesn't s*** or get off the pot, he'll dismiss it.

Our Lamar sources says there's bad blood on both sides. It's not as if he's begging her to reconcile ... he feels betrayed by Khloe as well. The Lamar sources say she's told him he has to make some sort of "grand gesture" before they can go the next step, and so far he's not willing to do it.

For her part, we're told she has "a big heart" and doesn't want to hurt him by sealing the deal on the divorce. But it's more than just mercy ... we're told she still has feelings for him.

As for the pic Khloe posted showing her "LO" tattoo on a gearshift ... we're told it's not a sign she's going back with Lamar ... she just digs her new Bentley.