Russell is the great-grandson of former Prime Minister Stanley Baldwin. The former Oxford University student is now a deer farmer living in Dorset.
The photo, taken in 1979, shows the still-single Lady Diana Spencer relaxing with Russell after they had been injured on a group ski holiday in Val Claret in the French Alps, Australia's Telegraph newspaper said.
"They kept each other company while the others went skiing and at the end of the holiday Adam was somewhat smitten but absolutely nothing happened," Morton told ITV News.
"He left unspoken the fact that he hoped the friendship between himself and Diana could be renewed and developed upon his return. When he arrived home a year later it was too late. A friend told him: 'You've only got one rival -- the prince of Wales.'"
The picture was sold to the Daily Mirror in 1981, two days after Diana's engagement to Prince Charles was announced, but the publication never ran it. The photo, on which the newspaper's staff wrote "not to be published, is being auctioned off in the United States, Britain's Daily Telegraph said.
Diana's marriage to Charles ended in divorce in 1996. She was killed in a Paris car crash in 1997.