The joint artwork titled 'Ladylike' was unveiled by The Libertines band's vocalist Doherty at an exhibition earlier this year.
It is now set to be the showpiece lot at an auction of his belongings, reported Daily Star online.
Other items going under the hammer include a selection of the rocker's guitars, stage outfits and lyric books.
A portion of profits from the sale will be donated to The Amy Winehouse Foundation, a charity set up after the singer's death last year.