Autographed ‘To Derek Peace + Love John Lennon 1969’, the framed picture is a sketch of Lennon and Yoko Ono in John’s characteristic caricature style.
Derek was the uncle of vendor Frank Massie, who inherited the work from his late father, also called Frank, who was passed it when Derek died.
The work will go under the hammer in Richard Winterton Auctioneers’ Antiques & Home Sale on Monday, November 1, from The Lichfield Auction Centre at Fradley Park, starting at 9.30am.
Mr Massie said: “My Uncle Derek was given this autograph and sketch personally by John Lennon when he visited Durness in the far north of Scotland with Yoko Ono, Julian Lennon and Yoko’s daughter Kyoko in 1969.
“John used to go there nearly every summer when he was a child, together with visiting his relatives from Edinburgh, and he said it was one of his favourite places in the world.
“My uncle lived and worked in Durness and met John while he was there.”
It was around this time that Lennon crashed his Austin Maxi near Loch Eriboll on the north coast of Scotland, cutting short their visit and landing the Beatles star in hospital for five days.
“My father Frank inherited the picture when my uncle died and it was then passed to me when my dad died,” added Mr Massie.
“It was originally in an old frame but I have had it re-framed.
“I’m nearing the end of my life so I've decided to sell it and get the best possible price on behalf of my children.”
Lennon took childhood summer holidays in Durness and the song In My Life from 1965 Beatles album Rubber Soul is said to be based on a poem about the village penned whilst holidaying in the area as a teenager.
The village of Durness has a memorial garden to Lennon featuring stones engraved with In My Life lyrics, although the house where he stayed as a boy has now been demolished and replaced with a modern dwelling.
“John Lennon was one of the most iconic figures of the 20th century,” said ephemera specialist Robert French.
“His work with The Beatles, peace activism, solo career and tragic untimely death in New York have been intricately documented and he remains a source of fascination and inspiration for millions of people worldwide.
“Lennon’s love of Scotland started in his childhood and he wanted to share these formative memories with Yoko when they first became a couple.
“This drawing links these great loves of Lennon’s life and demonstrates his affection to his personal friends and acquaintances.
“We’ve guided this cautiously at £500 to £800 but there’s a strong possibility it could fetch between £2,000 and £4,000.”
The November 1 auction also features a football signed by Rod Stewart and an autographed frame of U2 memorabilia, both consigned by Mr Massie.
The auction catalogue will be online the week before the sale and can be viewed via www.richardwinterton.co.uk/auction-dates.