The drawing is part of a set of 18 previously unpublished letters he wrote to Evelyn Kendall, a close friend and fellow student from the Royal College of Art, London, in which he describes, in detail, his daily routine.
The letters, some of which run to 12 pages, were unknown until Miss Kendall's daughter took them to the BBC television programme Antiques Roadshow. Included in a big sale of English literature and history at Sotheby's on 15 July, they are expected to fetch up to pounds 350,000 at auction.
Moore and Kendall were friends during the 1920s, and although she was said to have harboured "expectations" from the relationship, they did not marry and she was believed to have been disappointed.
In one of the letters, Moore included a rough pen and ink sketch of himself reading one of her letters, surrounded by nude models "waiting on the common for a job". He also drew sculptures - "all the works I haven't done" - and pointed out a large inky blotch which, he said, was a "failed" attempt to draw Miss Kendall.
The sculptor wrote oftenabout his attempts at "carving" and his hopes of producing something "of which I'll not be ashamed". He told her his plans for Christmas and a visit to the dentist. In another letter he described his routine and confessed he loved talking about "myself and sculpture in particular".
He writes: "Yesterday I began the bust of Betty (sisters dont [sic] make good models - they lack obedience). I could make a good thing of this head of Betty, given enough time & no spectators. As we approached Braconash there was one [tree] cut down - it was a wonderful piece of sculpture, one yard of it especially - which I'd like to cutout, place on a base to keep near me when I'm working, perhaps call it Fecundity, forat [sic] the front it has two large swellings which burst through the large mass like the breasts of a huge primitive woman.
"I get up about 9 - begin carving about 10 - carve for an hour then stretch my legs by getting a pear or two from the pear tree, then carry on till 12.30 ... Carve again till 4."
Peter Beal, of Sotheby's, said: "These letters are a major discovery. No one even knew they existed. They are so vivid and give such insight into what he was doing at the time and how he liked to work."