My B always seems to rub both sides of his face into the sofa after he eats. Is he using it as a napkin? LOL! He also liked rubbing his face into the Christmas tree when I had it up. (It was an artificial tree)
I should mention that he's 16 years old, and only started doing this 2 Christmases ago.
Yes…. perfect call... napkin!!! or considering his age, he may have a tooth or two that is bothering him....
Yeah, you really do need to supply napkins! My guy likes to rub his face on whatever is handy, especially if he has had a messy treat. Then he might do a proper clean up like a cat…...lick the paws, wipe the face, rinse, repeat. 
If he has had some teeth removed, he may have food stuck in between the teeth and/or the gum. My elderly girl is the only one of my Bs who does this and she has had teeth removed. This happens a couple times a week and I use my finger to help loosen and remove the food.
Jennifer
When you mentioned his age I too immediately thought of tooth issues. However any Basenji may do this to spread the scent. If it were me I'd just check his mouth though.
Shaye is 3, and she also does this - she is kind of a messy eater, carrying food away from the bowl and dropping pieces along the way to be picked up on her way back to the bowl, and she inevitably gets food around her mouth while digging into it. When she's done eating she "washes" both sides of her face with her paws but then comes and wipes it further on us, the furniture, or whatever suits her fancy, so it is likely he's using the couch as a napkin since he's older and it's less effort to do it that way. But, checking his teeth is a good precautionary move, and maybe helping to loosen stuff if he has missing teeth.
Maybe try brushing his teeth after he eats? I agree, if this is a relatively new habit, it may be teeth related…..but I am not clear about whether the face rubbing in the couch is new, or just the Christmas tree rubbing? If he has always rubbed his face in the couch, I would just say typical Basenji.
Becca is about 6 years old and has always done this. In the morning when she gets up she stretches then rubs her face on the carpet to rub the sleep out of her eyes. Then after she is finished eating (especially something really tasty) she will run to the rug and rub her face again then paw at her cheeks and lick her paws to make sure she doesn't have any crummies on her face.
He's not missing any teeth, and he doesn't seem to have any loose teeth or discomfort. I'm a dental hygienist, so I'm always checking his teeth. He has no trouble eating dry dog food or gnawing on his treats.
I have had some who do it, some who don't. Always good to check the teeth. In fact, a good idea to check and to start brushing their teeth regularly when young. I find it alarming that nearly half of all dogs have dental issues by about 3 yrs of age. My dogs always had perfect teeth til they died, but I used to feed RMB. Now, ugh. Fortunately Cara is a nut job who actually LOVES to have hers brushed. Arwen has learned to tolerate it.
I can honestly say that I was NOT the greatest at teeth with my first Basenjis… and I can tell you that I learned a hard lesson on how important it is not only to brush (and I swear by Placque Off but I still brush at least 5 times a week) but to make sure that the teeth are checked and if there is any question a closer check is needed...
AJ washes his face like a cat.
And yes, teeth are very important. I got AJ at five years old. He has had seven teeth pulled since I've had him and his breath is finally tolerable.
My 9.5 months old does that too. He rub his face in the carpet, and roll around there with his face and putting his paws up behind his ears after eating.
