Written neatly in blue ink, the incomplete manuscript containing 19 lines was bought by a fan from a flea market stall in London's Portobello Market in 1971, three years after the single was recorded.
The manuscript being offered at a pop memorabilia sale at Christie's auction house in London on April 30 includes two versions of the song, Reuters reports.
The page is also missing the final verse of the released version of the song, which spent two weeks as No. 1 on the British Record Retailer charts and nine weeks in the top spot on the U.S. Billboard charts when it was released in August 1968.
According to Christie's, McCartney had difficulty completing the song.
"John and Cynthia were splitting up, and I felt particularly sorry for Julian. I thought as a friend of the family, I would motor out to Weybridge and tell them that everything was all right -- to try to cheer them up, basically, and see how they were.
"I had about an hour's drive. I would always turn the radio off and try and make up songs. I started singing, 'Hey Jools -- don't make it bad, take a sad song and make it better.' It was optimistic, a hopeful message for Julian," McCartney wrote.
McCartney said he later changed the lyric to "Hey Jude" after a character in the hit musical Oklahoma! because it gave the song a more Country and Western feel.