I suppose it is possible - you could reline the barrel and recut the chamber for 5.56, or use a 5.56 barrel blank to machine a new SKS profile barrel, but then you would have to fabricate a 5.56 bolt and magazine follower. The only other engineering challenge remaining would be the recoil spring/s.
I've been gunsmithing/armorer-ing since 1973 and I have not seen an SKS in Nato 5.56 caliber, but it would not be impossible to do. If I were to attempt it, I would go for a .750 diameter 5.56 barrel blank and profile it/chamber it on the lathe. The bolt would be a milling exercise, and I would try to see if it would cycle reliably at that point. It's possible that the gas pressure in the SKS gas system would be enough using this caliber to operate the action without short stroking. It's my guess that the recoil spring weight would have to be reduced.
If this beastie exists, I'd like to see some detailed pictures.