This painting depicts Daidō Ichii (1292–1370), a Zen priest in the Shōichi branch of the Rinzai school. The inscription by Shōkai Reiken (d. 1396) of the Taikōan cloister at Tōfukuji Temple tells us that the painting depicts the anecdote of Daidō’s taming and befriending a deer and a swan. It is likely a work by the Tōfukuji painter-priest Minchō (1352–1431).
 
TANIGUCHI KoseiEnglish by Mary Lewine 
Buddhist Art Paradise: Jewels of the Nara National Museum. Nara National Museum, 2021.7, p.333, no.198. 

Priest Daidō Ichii (1289-1370) was born in Izumo (today's Shimane prefecture). He became the 28th abbot of Tōfuku-ji temple and later the 31st abbot of Nanzen-ji temple. Later on, he founded Ankoku-ji temple in Awaji. Among his disciples in Ankoku-ji temple, Kissan Minchō (1352-1431) is well known. Minchō became a Buddhist artist and at the same time was in charge of the Butsuden hall in Tōfuku-ji temple.
The inscription at the top of this portrait is by Priest Shōkai Reiken who was the 43rd abbot of Tōfuku-ji temple. According to the inscription, Priest Shōkai Reiken apparently wrote the inscription on the request of the feudal lord of Awaji, Hosokawa Mitsuharu, in 1394. Judging from the painting style and the historical background, the artist who painted this portrait must have been Minchō. This portrait is not an object for worship services. It describes Priest Daidō Ichii and his character, who is said to have taught Buddhist ideas even to animals. The priest, who is seated on a rock seat under a pine tree, and a white bird and a deer attending the priest are drawn with lively brush strokes and shadings. 
Masterpieces of Nara National Museum. Nara National Museum, 1993, p.67, no.50.