Note: Correction appended.

A rare Stradivarius cello is expected to set a world record when it goes to auction this fall. The cello, which was owned for decades by the British cellist Amaryllis Fleming, is being sold by the online instrument auction house Tarisio and carries an estimate of $1.75 million to $2.3 million. Made in 1717, the instrument is one of only 60 extant Stradivarius cellos.

The current record for a cello at auction is $1.288 million, which was set by a Stradivarius cello at Sotheby’s in 1988. In recent years, prices for such cellos in private sales have escalated dramatically. The “Duport” Stradivarius, which was owned during his lifetime by Mstislav Rostropovich, was purchased recently by the Nippon Music Foundation, an organization in Japan that loans instruments to musicians. Trade publications have reported the price as $20 million, the director of Tarisio, Jason Price, said.

The Amaryllis Fleming cello was made from the same “B-form” pattern as both the “Duport” cello and Yo-Yo Ma’s “Davidoff” cello.

Mr. Price and his partners, Dmitry Gindin and Christopher Reuning, started Tarisio in 1999. They believed that musicians, who will generally pay more for an instrument than dealers will, would feel more comfortable bidding online than in an auction room.

“It’s incredibly intimidating, if you’re a newbie, to sit or stand in a room filled with dealers and raise your hand,” Mr. Price said. “We felt the online platform was easier, more convenient, and a little more anonymous.”

Tarisio now has $10 million in annual sales of musical instruments, surpassing Sotheby’s and Christie’s.

The cello is being sold by the Fleming family to benefit the Royal College of Music. Tarisio is handling the sale in association with the London violin dealership J. & A. Beare Ltd. It will tour the cello for viewings to London, Cremona, Boston, and New York. Online bidding, at tarisio.com, will open October 1 and will end October 31 at 1 p.m. Eastern time.