There is evidence that cells can exchange mitochondria. There are some donor cells that transfer mitochondria to recipient cells via cytoplasmic nanotubes (within the same species). This happens endogenously and triggering factors may include stress.
On interspecies mitochondria transfer.
In a study by Yang and Koob, the feasibility of mitochondrial transplants was studied. Mitochondria isolated from donor cells were initially injected into mouse oocytes/embryos. Then mitochondria, along with a chunk of cytoplasm and membrane was taken out; these cell-like structures were called mitocytoplasts. Then, these mitocytoplasts were fused with recipient cells (mouse rho0 cells - these lack mitochondria) with the help of a viral fusion protein.
They found that the recipient cells supported mitochondria from the same species (donor species include mouse, rat, Mongolian gerbils and Golden Syrian hamsters).
The success of the "mitochondrial xenograft" depends on how different the species are and as shown in the abovementioned experiment, a donor cell (mouse) would not support the mitochondria from even a closely related species (rat). This incompatibility would primarily be based on the dependency of mitochondria on the nuclear genome which may be different for different species. It is possible that "mitochondrial xenografts" may be accepted; the impossibility of it has not been exhaustively verified.