The 1903 painting will be in Sotheby's sale of 70 Impressionist and early Modern paintings owned by the late Donald and Jean Stralem, which is expected to total more than £25m.
The "Blue Period" work is the most important Picasso to appear at auction for five years, comparable to Yo Picasso , a self-portrait which sold at Sotheby's in 1989 for just under £29m.
The last Picasso "Blue Period" painting to be auctioned was Maternit, which sold for £13.6m at Christie's New York in 1988.
The Absinthe Drinker is one of many important French works gathered over 50 years by Mr and Mrs Stralem, who married in 1928. Mrs Stralem was the granddaughter of the well-known banker and collector Philip Lehman and an active charity worker. Their collection was a collaborative effort and has rarely been exhibited outside New York. Mr Stralem died in 1976; the two-day sale on 8 May follows Mrs Stralem's death in December.
It also includes two Matisse paintings, The Hindu Pose, depicting a model shown as an odalisque semi-nude in front of brilliantly coloured patterned wallpaper and estimated at £5.5m, and Girl at the Piano, estimated at £4m.Reuse content