The original boat was used by Cook for his voyage to Australia and New Zealand, from 1769-71.
Unique Auction House in Lincoln will offer this replica with an estimate of £80,000-120,000.
It was built in 1993 and is reported to have cost £3m to build. The boat has been sold a number of times and its current owners bought it in 2006. For the past decade it has been leased out for events including re-enactments, weddings and parties.
Terry Woodcock, chief auctioneer and valuer at Unique, said the boat could “offer a lucrative business proposition to an investor” and said the cost of building a similar boat today would be in excess of £9m.
Endeavour is currently in Teeside and is offered alongside a pleasure cruiser The Teesside Princess - both being sold by the same consortium of investors.
The pleasure cruiser, which carries an estimate of £150,000-250,000, has a capacity of 120 people plus crew.
The auction will take place on August 28 at 10.30am. Online bids will not be accepted and a bond of £5000 is required to bid.