The handwritten letter by the former Beatles is set to go under the hammer in Los Angeles at the Profiles in History auction on December 18.
In the draft letter, dated September 29, 1971, Lennon asks Clapton to start a band with him, writing: "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."
Clapton played in John Lennon and Yoko Ono's Plastic Ono Band in 1969 before The Beatles' official split in 1970. He also played on The Beatles' "While My Guitar Gently Weeps" on the so-called "White Album", NME reports.
"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," auctioneer Joe Maddalena said.