This is a copy after Horace Vernet's Portrait of Bertel Thorvaldsen. The original by Vernet is in the Thorvaldsen Museum, Copenhagen (oil on canvas, 99.8 x 75.2 cam, signed and dated 1835). A replica by Vernet is in the Metropolitan Museum of Art, New York, see French Paintings: II, XIXe Century Catalogue, New York, 1966, p. 18, cat. n. 62, ill. p. 254. Another copy by Schenstrom is in a private collection in Copenhagen.
The bust being modeled in the painting is of Vernet.