It measures 5 x 3½in (13.5 x 9cm) and is inscribed Ye Owly Pusseycatte, a new Beast found in ye Island of New South Wales.
The animal wears a settler’s wide-awake hat with two peacock feathers and smokes a churchwarden pipe.
Lear later wrote The Owl and the Pussy Cat as a Christmas poem for his friend’s sick daughter, publishing it a few years after in 1871.
The watercolour is one of the pieces on offer at Guy Peppiatt’s Exhibition of British Drawings and Watercolours.
It runs from May 15-June 9 at Peppiatt’s Mason’s Yard gallery and includes more than 60 works spanning from the 1770s to the 1860s, considered the Golden Age of British watercolour painting.
Ye Owly Pusseycatte is a highlight of the exhibition and is thought to be the first representation by Lear of the later poem. It is available for £11,000 and is one of nine Lear works on offer at the show.
Pictures are also available from artists such as John Frederick Lewis, John Gardner Wilkinson and Anna Alma-Tadema.