The auction of ‘Head of a Bear’ will be held at Christie's auction house at 5pm.
It is among just a few of the Italian’s drawings which remain privately owned.
Dating back to the 1480s, the work of art is part of a collection of the artist’s small-scale animal drawings.
The masterpiece was achieved using silverpoint on pale pink-beige paper.
Laetitia Masson, an expert in old master drawings at Christie's, said silverpoint is a “very difficult technique, because it doesn't really admit any mistake”.
There is a lot of skill in the method as the drawing is achieved with a silver stick being applied to a specially prepared paper to leave marks and lines.
She added da Vinci was “fascinated by nature and animals in general”.
British painter and collector Sir Thomas Lawrence previously owned the special piece.
Later, it was sold at Christie's for £2.50 in 1860 - a small fraction of what it is expected to fetch on Thursday.