Do you see any redness or pinkish color between his toes or on the back of his legs just above his paws? If so he could have a yeast infection especially if you live in a wet climate.
Our Basenji mix is prone to this condition because we live in a damp climate and he is constantly liking his paws during rainy season. I have been giving him a probiotic and plain yogurt daily and this has helped keep the condition under control but he does have flareups every so often. When that has happened and I can't get him to stop licking I slip on a pair of baby socks and secure with a piece of bandage tape. And the cone of shame helps as well.
Apart from the possible yeast infection mentioned by Dreamskape, it's probably normal Basenji behaviour. They are pretty obsessive with cleanliness. Mine always has pristine feet (top and under). I would NOT recommend baby wipes. Firstly, they're coated with chemicals (artificial fragrance, etc) which sensitive breeds like basenjis don't need, and secondly, they're extremely bad for the environment and plumbing. Just keep towelling yr basenjis feet off with a cotton towel if they're wet or dirty. Enjoy the many quirks of the basenji as you get to know your pooch!
This is perfectly normal Basenji behaviour ! They clean themselves (and each other). I have a photo somewhere of a line of five Basenjis in a conga-line, each cleaning the one in front. We've been for a particularly muddy walk as I recall.
Daily, I get two filthy dirty Basenjis into the car in the woods, sometimes they appear to be wearing Wellington boots. But the drive home takes only about 20 minutes and two beautifully clean Bs leap out.
Keep an eye out for inter-digital cysts - but feet cleaning is nothing to worry about.
I would NOT recommend baby wipes. Firstly, they're coated with chemicals (artificial fragrance, etc)
I should have said I use ONLY hypoallergenic wipes... no fragrance, no alcohol, etc. I've used baby wipes for my dogs -- Rotties, Chows, basenjis, samoyeds-- for 27 years, the same I used for my supersensitive baby.
Thanks, btw, it sent me on a quest for ratings. Sadly, since I'm in Israel, I have on found generic and Huggies. But it's nice to have an updated evaluation on them.
On "eco friendly"... I'll wait for the research. I know there was a lot of debate on cloth vs disposable diapers. I would need to see a study that the water usage, detergents, etc actually aren't worse on the environment than wipes, especially the faster biodegradable wipes.