John Lennon held out the promise he could bring out more musical greatness in legendary guitarist Eric Clapton in a letter that could fetch as much as $30,000 when it is sold at auction next month, the organizers of the sale said on Monday.

The signed, hand-written letter by the Beatle, who died in 1980 at the age of 40, is one of a selection from some of the world's great musicians that will go under the hammer in Los Angeles at the Profiles in History auction on December 18.

In a draft letter dated September 29, 1971, Lennon expressed his respect and admiration for British guitarist Clapton and suggested that they form a band together.

"Eric, I know I can bring out something great, in fact greater in you that had been so far evident in your music. I hope to bring out the same kind of greatness in all of us, which I know will happen if/when we get together," Lennon wrote in the letter.

The letter will hold special significance for Beatles fans as auctioneer Joe Maddalena said it was widely known that there were problems in the Fab Four's relationships with each other, and that Clapton had almost become a Beatle.

Clapton played in the Plastic Ono Band, formed by Lennon and Yoko Ono in 1969 before the breakup of the Beatles in 1970. He also played on the George Harrison song "While My Guitar Gently Weeps", which was on the Beatles' White Album.

"There was a point in time when George Harrison thought about leaving the band and his replacement was Clapton, so this letter is a link of what could have been," Maddalena said.

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The letter is one of 300 manuscripts and letters from literary, musical and political greats, that will be auctioned from the holdings of an American collector.

"What we know of history is from the written word, without these letters, it would all be verbal. It's a really unique area of collecting as you're getting a glimpse into people's minds," Maddalena said.

Other highlights include a handwritten letter from George Washington, with a pre-sale estimate of up to $300,000, and a Charles Dickens manuscript with an obituary of novelist William Thackeray, expected to fetch between $40,000 and $60,000.

Also on the auction block is a signed, handwritten letter from German composer Ludwig van Beethoven to Tobias Haslinger, a friend of his publisher, in which the musician discussed the second performance of his Ninth Symphony and the Missa Solemnis, two of his most revered works.

The letter, written in German, is undated, but both the Ninth Symphony and Missa Solemnis debuted in performances in 1824. Because of the rarity of the letter, it is estimated it will sell for between $40,000 and $60,000.

Other items going under the hammer include a signed letter in Russian by composer Peter Ilyich Tchaikovsky, which has a pre-sale estimate of $10,000 to $15,000, and a letter by composer George Gershwin dated March 24, 1932, in which he compares his compositions "Rhapsody in Blue" and "An American in Paris".

The Gershwin letter is expected to sell for as much as $3,000, according to the auction house.