An oil painting by Thomas Gainsborough is set to fetch more than £2million when it is auctioned in America next month.

The picture, entitled The Blue Page, was painted by Sudbury-born Gainsborough sometime between 1770 and 1772 when he was in his early 40s and after he left Ipswich for Bath.

Now nearly 250 years later the picture is expected to sell for between $3-4million – between £2-2.6m – when it is auctioned at Sotheby’s in New York on January 27. And if it does sell for anything like those sums it will become the fourth or fifth most valuable work by Gainsborough sold at auction.

Auctioneers Sotheby’s say of The Blue Page: “Thomas Gainsborough shows an extraordinary fluency, speed and assurance in this canvas. The artist must have treated this as a private piece, uncommissioned and investigative, an experiment in formal picture-making that showed all his ability in his arrangement of the composition and demonstrated his genius as a colourist.

“The canvas was painted during his later years in Bath. He had visited Bath in the autumn of 1758 to see whether the continual flow of tourists to the spa would provide greater possibilities for portrait commissions and decided there was.

“He returned to Ipswich, sold or gave away his possessions and moved his family to the West Country.”

Sotheby’s reckon Gainsborough painted The Blue Page sometime between 1770 and 1772 and after he had painted, in 1770, a similarly-titled picture, The Blue Boy, now owned by The Huntington Library and Art Gallery in San Marino, California.

The Blue Page has changed hands several times since the 18th Century. Its previous owners include the fourth Earl of Egremont; French nobleman Comte Boni de Castellane; wealthy South African diamond and gold mine owner Sir Joseph Robinson and, most recently, by the late American billionaire businessman Adolph Alfred Taubman, who once owned Sotheby’s.

Mr Taubman bought The Blue Page in 1989 and owned and treasured it until his death, at the age of 91, on April 17 this year.