The mount labels it "? Raphael", and the Ashmolean website lists it as copy after Raphael, but it is in a box with authentic Raphaels. The 1956 (reprinted 1972) catalogue by the excellent Karl Parker states that "there can be no doubt at all that it is a copy" (no. 665, p. 352). Parker was a perceptive scholar and is an excellent guide to Raphael, but he was abstemious in attribution. In the catalogue of the 1983 Raphael drawings exhibition at the British Museum, J.A. Gere and Nicholas Turner conclude that it is a copy by Penni.
On the other hand, Paul Joannides states that the attribution "is controversial, but needlessly so, for its inventiveness, both of arrangement and drawing style, is quite beyond any of Raphael's pupils" (The Drawings of Raphael, University of California Press 1983 p. 124 - cat. 453 and plate 46). Joannides is probably the most eminent scholar of Raphael drawings, and I have found him an indispensable guide. But I think he's wrong on this one.
The woman's face is picked out with shading that closely imitates Raphael's style, but lacks his subtlety. The drapery over the legs is not well related to the rest of the drawing, which becomes particularly apparent when you view it upside down, to get a sense of the tonal relationships. Gere and Turner are right to criticise inconsistency of touch, with excessively dark shadows. The elbows in particular lack Raphael's ability to capture light and shade. Even in the reproduction above you can see the dark lump marking the elbow of the suckling child on the left.
Joannides is impressed with the foreshortening. I'm not. The arm of the child on the right seems almost foreshortened in reverse. The forearm is excessive large and prominent, although it recedes from the picture plane. It's noteworthy that this is a divergence from the completed fresco (below), where it continues straight rather than twisting down. The contrapposto of this figure is also more awkward in the drawing.
Condition was not discussed by the sources I cite above. There is some wear, particularly in the standing child. It is at least plausible that this is a Raphael re-worked by an assistant. Indeed, the very quality of finish speaks against Raphael's authorship; it reads more as a highly polished work of art in its own right rather than a working study, and Raphael's drawings seem always to be working studies. However, there is insufficient variety of style and handling to conclude that two artists of markedly different ability worked on this sheet, and I don't think there is sufficient evidence to attribute even tentatively to Raphael.
It's easier to make the case against this being by Raphael than to make the positive case for another attribution. The attribution to Giulio Romano has generally been dismissed, partly because the drawing is so close to Raphael, and Giulio was a more distinctive personality. He continued to be a very prolific draughtsman after Raphael's death, but abandoned chalk medium - maybe because he couldn't meet Raphael's standard. To my eyes, the handling of the face in particular is close to Giulio. It seems to me plausible to speculate that this was an example of Giulio following Raphael unusually closely, but that must remain mere speculation; there is no strong visual evidence for his authorship. The attribution to Penni is perhaps more likely, but this drawing seems to me to good to be Penni's. Parker's 'After Raphael' seems right.