Ningyo no Mori (1984)

Blurb:
Legend has it that if a human eats a mermaid’s flesh, they will be granted eternal life. But is that a blessing or a curse? Immortal lovers Yuta and Mana travel through Japan and the centuries longing for a normal life. On their journey, they meet others who have consumed the flesh of a mermaid in hope of becoming immortal. But the powerful substance affects each person differently. Yuta and Mana are two of the lucky ones. Others are fated to die or transform into a savage monster, a "lost soul." Mermaid Forest contains three of Takahashi’s uniquely macabre mermaid tales, A Mermaid Never Smiles, The Village of the Fighting Fish, and Mermaid Forest. Each revolves around Yuta, who wanders for hundreds of years, seeking a mermaid to cure him of his immortality.

Source: www.anisearch.com/manga/1010