Is this work a study of a young woman, produced with the help of one of the most sought-after female models in Montmartre? Given that she posed for all the artists in Montmartre, it is more than likely that she posed for Steinlen, almost certainly between 1884 (when she met Toulouse-Lautrec) and 1894 (when, on the advice of Degas, she took up her artistic career full time).
Is it the portrait of an acquaintance of Steinlen, whom the artist knew well? He only rarely agreed to commissions for portraits, preferring to “sketch” the faces of the people who filled his professional and private life. This could be a portrait of the muse of Toulouse-Lautrec, Erik Satie, and others (and known to the artist), in which case the portrait could date from 1887-1893.
Or could it be a portrait of the young painter for herself - a young artist who, like him, was interested in the depiction of the lower classes of Montmartre and who enjoyed success from 1892-1894? This could explain the attention paid to the model’s determined and deliberate expression, similar to that of another portrait of Suzanne Valadon by Steinlen from 1896; the age of the young woman seems to be about the same as that in the Musée de Vernon’s portrait.
Without knowing the history of the work in more detail, this last hypothesis seems just as likely, even if the exact nature of the relation between the discreet Steinlen and the volcanic Suzanne is still to be studied ...