This paper proposes a new voice conversion (VC) task from human speech to dog-like speech while preserving linguistic information as an example of human to non-human creature voice conversion (H2NH-VC) tasks. Although most VC studies deal with human to human VC, H2NH-VC aims to convert human speech into non-human creature-like speech. Non-parallel VC allows us to develop H2NH-VC, because we cannot collect a parallel dataset that non-human creatures speak human language. In this study, we propose to use dogs as an example of a non-human creature target domain and define the "speak like a dog" task. To clarify the possibilities and characteristics of the "speak like a dog" task, we conducted a comparative experiment using existing representative non-parallel VC methods in acoustic features (Mel-cepstral coefficients and Mel-spectrograms), network architectures (five different kernel-size settings), and training criteria (variational autoencoder (VAE)- based and generative adversarial network-based). Finally, the converted voices were evaluated using mean opinion scores: dog-likeness, sound quality and intelligibility, and character error rate (CER). The experiment showed that the employment of the Mel-spectrogram improved the dog-likeness of the converted speech, while it is challenging to preserve linguistic information. Challenges and limitations of the current VC methods for H2NH-VC are highlighted.