The silver mounted DB flintlock tap-action weapon with attached 69.4cm blade was made by HW Mortimer in 1805.
The weapon was discovered in a collection of his possessions owned by his closest friend Alexander Davison, the 'Daily Mail' reported.
"This is a truly exceptional piece of British history with a very interesting back story.
It is a very fine, rare item in its own right," Ben Gamble, head auctioneer at Cuttlestones, said.
"Pistols of this period and quality and by makers of this calibre do not often come up for sale and its links to Nelson are only set to broaden its appeal," he said.
"To say we're excited by the prospect of selling this piece is an understatement. All the evidence said it did belong to him and came back from Trafalgar with Hardy, the captain of the Victory.
"The likelihood is Nelson would have used it in Trafalgar," said Gamble.
He said the sword-pistol was battle-worn and had suffered some damage, but could be made to work again by a good gunsmith.
Nelson joined the Royal Navy at the tender age of 12 through the influence of his uncle Maurice Suckling and was given command of his first ship more than 20 years later.
He lost his right eye and right arm on active service but continued to inspire his men in subsequent battles, three of which were the most decisive in British history.
During the Battle of Trafalgar, Nelson was hit by a French sniper and mortally wounded, the report said.