A hybrid of swine influenza virus and that of birds is thought to have been the cause of the deadly 1918 human influenza pandemic. No human BLV infection has ever been found. Paradoxically, BLV virus grows very well on certain human cell cultures in the laboratory. Contact between farmers and their cattle is certainly close enough to have given at least one opportunity for natural infection. The supply of human organs for transplantation is insufficient to meet the demand.
Xenotransplants are far too dangerous for our species to even consider.
That leaves artificial organs. Surgeons have decades of experience with artificial implants. None of them are contagious so there is no risk of transmission to anyone. Perhaps the production of reliable artificial organs will take time, but scientists are much closer to making artificial organs than they are to inventing the Star Trek diagnostic tool.