Rumours suggest they reformed in April 1976 for a 'secret' recording session in Los Angeles, but the planned album was never officially released.
David Bedford, of the British Beatles Fan Club, believes Lennon would have still been bitter about the split when he wrote the letter.
Shortly after, he penned the song 'How Do You Sleep at Night?' about Paul McCartney.
Mr Bedford said: "Things had been falling apart for a while but they hung around until the beginning of 1970 so they could release their final album, Let It Be.
"But the tone of the letter is dismissive almost. The bulk of it is about Yoko, and John doesn't seem to be treating the stories seriously.
"He's almost saying 'by the way it's not true, just tell your guys to stop spreading rumours'."
Mr Bedford believes Lennon was feeling a "lot more positive" about a reforming the band later on in the decade.
He added: "If the band had reformed it would have been a personal challenge for John."
Paul McCartney never made public his feelings on reforming the band, but George Harrison, when asked, in 1981, if he was keen on the idea, said: "We can't, John's dead."
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